El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro

In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ α, β ≤ 1 and p ∈ Z ^{+}, in the standard, anisotropic and weighted Sobolev spaces...

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Autores:: Albarracin Hernandez, Carolina

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2021

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
dc.title.translated.eng.fl_str_mv	The Cauchy problem associated with a generalization of the Zakharov-Kuznetsov equation on the cylinder
title	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
spellingShingle	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro 510 - Matemáticas:515 - Análisis Cauchy problem Function spaces Functional analysis Problema de Cauchy Espacios funcionales Análisis funcional EDP Espacios de Sobolev Buen planteamiento local PDE Sobolev’s spaces Local well possednes
title_short	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
title_full	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
title_fullStr	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
title_full_unstemmed	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
title_sort	El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
dc.creator.fl_str_mv	Albarracin Hernandez, Carolina
dc.contributor.advisor.none.fl_str_mv	Rodríguez Blanco, Guillermo
dc.contributor.author.none.fl_str_mv	Albarracin Hernandez, Carolina
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas:515 - Análisis
topic	510 - Matemáticas:515 - Análisis Cauchy problem Function spaces Functional analysis Problema de Cauchy Espacios funcionales Análisis funcional EDP Espacios de Sobolev Buen planteamiento local PDE Sobolev’s spaces Local well possednes
dc.subject.lemb.eng.fl_str_mv	Cauchy problem Function spaces Functional analysis
dc.subject.lemb.spa.fl_str_mv	Problema de Cauchy Espacios funcionales Análisis funcional
dc.subject.proposal.spa.fl_str_mv	EDP Espacios de Sobolev Buen planteamiento local
dc.subject.proposal.eng.fl_str_mv	PDE Sobolev’s spaces Local well possednes
description	In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ α, β ≤ 1 and p ∈ Z ^{+}, in the standard, anisotropic and weighted Sobolev spaces in R × T and T^{2}. For this purpose, we use parabolic regularization, localized Strichartz and energy estimates, together with a compactness argument, as well as, commutator estimates and remarkable properties of the Stein derivative. In addition, we show the existence of certain type of solitary wave in the cylinder.
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-09-17T17:28:13Z
dc.date.available.none.fl_str_mv	2021-09-17T17:28:13Z
dc.date.issued.none.fl_str_mv	2021-07
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv	http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/TD
format	http://purl.org/coar/resource_type/c_db06
status_str	acceptedVersion
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/80230
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/80230 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.references.spa.fl_str_mv	[1] G. P. Agrawal. Fiber-optic communication systems, volume 222. John Wiley & Sons, 2012. [2] C. Albarracin and G. Rodriguez-Blanco. The IVP for a certain dispersion generalized ZK equation in bi-periodic spaces, 2021. [3] J. P. Albert. Concentration compactness and the stability of solitary-wave solutions to nonlocal equa tions. Contemporary Mathematics, 221:1–30, 1999. [4] J. Angulo, J. Bona, F. Linares, and M. Scialom. Scaling, stability and singularities for nonlinear, dis persive wave equations: the critical case. Nonlinearity, 15(3):759, 2002. [5] T. Aubin. Nonlinear analysis on manifolds. Monge-Ampere equations, volume 252. Springer Science & Business Media, 1982. [6] T. B. Benjamin. Internal waves of permanent form in fluids of great depth. Journal of Fluid Mechanics, 29(3):559–592, 1967. [7] H. A. Biagioni and F. Linares. Well-posedness Results for the Modified Zakharov-Kuznetsov Equation, pages 181–189. Birkhäuser Basel, Basel, 2003. [8] J. F. Bolaños Méndez et al. El problema de Cauchy asociado a una generalización de la ecuación ZK BBM. PhD thesis, Universidad Nacional de Colombia-Sede Bogotá. [9] J. L. Bona and R. Smith. The initial-value problem for the Korteweg-de Vries equation. Philo sophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 278(1287):555–601, 1975 [10] J. L. Bona and N. Tzvetkov. Sharp well-posedness results for the BBM equation. Discrete Contin. Dyn. Syst, 23(1241-1252):7, 2009. [11] E. Bustamante, J. J. Urrea, and J. Mejía. Periodic Cauchy problem for one two-dimensional generaliza tion of the Benjamin–Ono equation in Sobolev spaces of low regularity. Nonlinear Analysis, 188:50–69, 2019. [12] A. Cunha and A. Pastor. The IVP for the Benjamin–Ono–Zakharov–Kuznetsov equation in low regularity Sobolev spaces. Journal of Differential Equations, 261(3):2041–2067, 2016. [13] A. Cunha and A. Pastor. Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces. Journal of Differential Equations, 274:1067–1114, 2021. [14] L. Dawson, H. McGahagan, and G. Ponce. On the decay properties of solutions to a class of Schrödinger equations. Proceedings of the American Mathematical Society, 136(6):2081–2090, 2008. [15] O. Duque. Sobre una versión bidimensional de la ecuación Benjamin-Ono generalizada. Tesis de doc torado, Universidad Nacional de Colombia, Bogotá, 2014. [16] A. V. Faminskii. The Cauchy problem for the Zakharov–Kuznetsov equation. Differentsial’nye Uravne niya, 31(6):1070–1081, 1995. [17] G. Fonseca, F. Linares, and G. Ponce. The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces. In Annales de l’Institut Henri Poincare (C) Non Linear Analysis, volume 30, pages 763–790. Elsevier, 2013 [18] G. Fonseca and G. Ponce. The IVP for the Benjamin–Ono equation in weighted Sobolev spaces. Journal of Functional Analysis, 260(2):436 – 459, 2011. [19] S. V. Francis Ribaud. Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation. Discrete and Continuous Dynamical Systems, 37(1):449–483, 2017. [20] L. Grafakos. Classical fourier analysis, volume 2. Springer, 2008. [21] A. Grünrock and S. Herr. The Fourier restriction norm method for the Zakharov-Kuznetsov equation. arXiv preprint arXiv:1302.2034, 2013. [22] E. Hille. Methods in classical and functional analysis. 1972. [23] A. D. Ionescu and C. E. Kenig. Local and global well-posedness of periodic KP-I equations. Mathema tical Aspects of Nonlinear Dispersive Equations. Ann. Math. Stud, 163:181–211, 2009. [24] J. R. J. Iorio and W. V. L. Nunes. Introducao as equacoes de evolucao nao lineares. Cnpq/Impa, Rio de Janeiro, 1991. [25] R. J. Iório. KdV, BO and friends in weighted Sobolev spaces. In Functional-analytic methods for partial differential equations, pages 104–121. Springer, 1990. [26] I. J. Iorio Jr, R. J. Iorio Jr, and V. de Magalhães Iorio. Fourier analysis and partial differential equations, volume 70. Cambridge University Press, 2001. [27] R. José Iório, Jr. On the Cauchy problem for the Benjamin-Ono equation. Communications in partial differential equations, 11(10):1031–1081, 1986. [28] T. Kato. Quasi-linear equations of evolution, with applications to partial differential equations. Spectral theory and differential equations, pages 25–70, 1975. 118 Bibliografía [29] T. Kato. On the Cauchy problem for the (generalized) Korteweg-de Vries equation. Studies in applied mathematics, 8:93–128, 1983. [30] T. Kato and G. Ponce. Commutator estimates and the Euler and Navier-Stokes equations. Communi cations on Pure and Applied Mathematics, 41(7):891–907, 1988. [31] G. Keiser. Optical fiber communications. Wiley Online Library, 2003. [32] C. E. Kenig. On the local and global well-posedness theory for the KP-I equation. In Annales de l’Institut Henri Poincare (C) Non Linear Analysis, volume 21, pages 827–838. Elsevier, 2004. [33] C. E. Kenig, G. Ponce, and L. Vega. Well-posedness and scattering results for the generalized korteweg de vries equation via the contraction principle. Communications on Pure and Applied Mathematics, 46(4):527–620, 1993. [34] C. E. Kenig, G. Ponce, and L. Vega. A bilinear estimate with applications to the KdV equation. Journal of the American Mathematical Society, 9(2):573–603, 1996. [35] C. E. Kenig, G. Ponce, and L. Vega. On the unique continuation of solutions to the generalized KdV equation. Mathematical Research Letters, 10(5/6):833–846, 2003. [36] S. Kinoshita and R. Schippa. Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation. Journal of Functional Analysis, 280(6):108904, 2021. [37] H. Koch and N. Tzvetkov. On the local well-posedness of the Benjamin-Ono equation in Hs(R). In ternational Mathematics Research Notices, 2003(26):1449–1464, 2003. [38] D. Korteweg and G. de Vries. On the change of long waves advancing in a rectangular canal and a new type of long stationary wave. Philosophical Magazine, 39:422–443, 1835. [39] E. W. Laedke and K.-H. Spatschek. Nonlinear ion-acoustic waves in weak magnetic fields. The Physics of Fluids, 25(6):985–989, 1982. [40] D. Lannes, F. Linares, and J.-C. Saut. The Cauchy problem for the Euler–Poisson system and derivation of the Zakharov–Kuznetsov equation. In Studies in phase space analysis with applications to PDEs, pages 181–213. Springer, 2013 [41] F. Linares, M. Panthee, T. Robert, and N. Tzvetkov. On the periodic Zakharov-Kuznetsov equation. arXiv preprint arXiv:1809.02027, 2018. [42] F. Linares and A. Pastor. Well-posedness for the two-dimensional modified Zakharov–Kuznetsov equa tion. SIAM Journal on Mathematical Analysis, 41(4):1323–1339, 2009. [43] F. Linares and A. Pastor. local and global well-posedness for the 2d generalized zakharov-kuznetsov equation. Journal of Functional Analysis, 260 (4):1060–1085, 2010. Bibliografía 119 [44] F. Linares and A. Pastor. Local and global well-posedness for the 2D generalized Zakharov–Kuznetsov equation. Journal of Functional Analysis, 260(4):1060–1085, 2011. [45] F. Linares, A. Pastor, and J.-C. Saut. Well-posedness for the ZK equation in a cylinder and on the background of a KdV soliton. Communications in Partial Differential Equations, 35(9):1674–1689, 2010. [46] F. Linares and G. Ponce. Introduction to nonlinear dispersive equations. Springer, 2014. [47] F. Linares and J.-C. Saut. The Cauchy problem for the 3D Zakharov-Kuznetsov equation. RN, 1:2, 2009. [48] P.-L. Lions. The concentration-compactness principle in the calculus of variations. The locally compact case, part 2. In Annales de l’Institut Henri Poincare (C) Non Linear Analysis, volume 1, pages 223–283. Elsevier, 1984. [49] P.-L. Lions. The concentration-compactness principle in the calculus of variations. The limit case, part 1. Revista matemática iberoamericana, 1(1):145–201, 1985. [50] P.-L. Lions. Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models, volume 2. Ox ford University Press on Demand, 1996. [51] J. d. C. Lizarazo Osorio et al. El problema de Cauchy de la clase de ecuaciones de dispersión generalizada de Benjamin-Ono bidimensionales. PhD thesis, Universidad Nacional de Colombia-Sede Bogotá. [52] L. Molinet and D. Pilod. Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and appli cations. Annales de l’Institut Henri Poincaré (C) Non Linear Analysis, 32(2):347–371, 2015. [53] L. Molinet, J.-C. Saut, and N. Tzvetkov. Global well-posedness for the KP-I equation on the background of a non-localized solution. Communications in mathematical physics, 272(3):775–810, 2007. [54] A. Moliton. Solid-State physics for electronics. John Wiley & Sons, 2013. [55] J. Nahas and G. Ponce. On the persistent properties of solutions to semi-linear Schrödinger equation. Communications in Partial Differential Equations, 34(10):1208–1227, 2009. [56] M. B. Nathanson. Additive Number Theory The Classical Bases, volume 164. Springer Science & Business Media, 2013. [57] H. Ono. Algebraic solitary waves in stratified fluids. Journal of the Physical Society of Japan, 39(4):1082–1091, 1975. [58] J. A. Pava. Nonlinear dispersive equations: existence and stability of solitary and periodic travelling wave solutions. Number 156. American Mathematical Soc., 2009. [59] Y. Qin and P. Kaloni. Steady convection in a porous medium based upon the Brinkman model. IMA journal of applied mathematics, 48(1):85–95, 1992. [60] G. Rodríguez-Blanco. On the Cauchy problem for the Camassa-Holm equation. Nonlinear Anal., 46:309–327, 2001. [61] F. Sánchez Salazar et al. El problema de Cauchy asociado a una ecuación del tipo rBO-ZK. PhD thesis, Universidad Nacional de Colombia. [62] R. Schippa. On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations. arXiv preprint arXiv:1903.02027, 2019. [63] T. Tao. Global well-posedness of the Benjamin–Ono equation in H1(R). Journal of Hyperbolic Differen tial Equations, 1(01):27–49, 2004. [64] T. Tao. Nonlinear dispersive equations: local and global analysis. Number 106. American Mathema tical Soc., 2006. [65] V. Zakharov and E. kuznetsov. On three dimensional soliton. Sov.Phys-JETP Anal., 39(2):285–286, 1974
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dc.format.extent.spa.fl_str_mv	vii, 120 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Doctorado en Ciencias - Matemáticas
dc.publisher.department.spa.fl_str_mv	Departamento de Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rodríguez Blanco, Guillermo2812498adc8a2469e24651f995a011c5Albarracin Hernandez, Carolina64f70225db6d79b4695b98a03431e3632021-09-17T17:28:13Z2021-09-17T17:28:13Z2021-07https://repositorio.unal.edu.co/handle/unal/80230Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ α, β ≤ 1 and p ∈ Z ^{+}, in the standard, anisotropic and weighted Sobolev spaces in R × T and T^{2}. For this purpose, we use parabolic regularization, localized Strichartz and energy estimates, together with a compactness argument, as well as, commutator estimates and remarkable properties of the Stein derivative. In addition, we show the existence of certain type of solitary wave in the cylinder.En el presente trabajo, estudiamos cuestiones relacionadas al buen planteamiento local, del problema de valor inicial asociado a la ecuación diferencial parcial, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, donde 0 ≤ α, β ≤ 1 y p ∈ Z^{+}, en los espacios de Sobolev estandar, anisotrópicos y con pesos en R×T y en T^{2}. Para dicho fin, usamos regularización parabólica, estimativas de Strichartz localizadas y de energía, junto con un argumento de compacidad, como también estimativas del conmutador y propiedades notables de la derivada de Stein. Además, probamos la existencia de cierto tipo de onda solitaria en el cilindro. (Texto tomado de la fuente).Incluye índice alfabéticoDoctoradoDoctor en Ciencias - Matemáticasvii, 120 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas:515 - AnálisisCauchy problemFunction spacesFunctional analysisProblema de CauchyEspacios funcionalesAnálisis funcionalEDPEspacios de SobolevBuen planteamiento localPDESobolev’s spacesLocal well possednesEl problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindroThe Cauchy problem associated with a generalization of the Zakharov-Kuznetsov equation on the cylinderTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TD[1] G. P. Agrawal. Fiber-optic communication systems, volume 222. John Wiley & Sons, 2012.[2] C. Albarracin and G. Rodriguez-Blanco. The IVP for a certain dispersion generalized ZK equation in bi-periodic spaces, 2021.[3] J. P. Albert. Concentration compactness and the stability of solitary-wave solutions to nonlocal equa tions. Contemporary Mathematics, 221:1–30, 1999.[4] J. Angulo, J. Bona, F. Linares, and M. Scialom. Scaling, stability and singularities for nonlinear, dis persive wave equations: the critical case. Nonlinearity, 15(3):759, 2002.[5] T. Aubin. Nonlinear analysis on manifolds. Monge-Ampere equations, volume 252. Springer Science & Business Media, 1982.[6] T. B. Benjamin. Internal waves of permanent form in fluids of great depth. Journal of Fluid Mechanics, 29(3):559–592, 1967.[7] H. A. Biagioni and F. Linares. Well-posedness Results for the Modified Zakharov-Kuznetsov Equation, pages 181–189. Birkhäuser Basel, Basel, 2003.[8] J. F. Bolaños Méndez et al. El problema de Cauchy asociado a una generalización de la ecuación ZK BBM. PhD thesis, Universidad Nacional de Colombia-Sede Bogotá.[9] J. L. Bona and R. Smith. The initial-value problem for the Korteweg-de Vries equation. Philo sophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 278(1287):555–601, 1975[10] J. L. Bona and N. Tzvetkov. Sharp well-posedness results for the BBM equation. Discrete Contin. Dyn. Syst, 23(1241-1252):7, 2009.[11] E. Bustamante, J. J. Urrea, and J. Mejía. Periodic Cauchy problem for one two-dimensional generaliza tion of the Benjamin–Ono equation in Sobolev spaces of low regularity. Nonlinear Analysis, 188:50–69, 2019.[12] A. Cunha and A. Pastor. The IVP for the Benjamin–Ono–Zakharov–Kuznetsov equation in low regularity Sobolev spaces. Journal of Differential Equations, 261(3):2041–2067, 2016.[13] A. Cunha and A. Pastor. Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces. Journal of Differential Equations, 274:1067–1114, 2021.[14] L. Dawson, H. McGahagan, and G. Ponce. On the decay properties of solutions to a class of Schrödinger equations. Proceedings of the American Mathematical Society, 136(6):2081–2090, 2008.[15] O. Duque. Sobre una versión bidimensional de la ecuación Benjamin-Ono generalizada. Tesis de doc torado, Universidad Nacional de Colombia, Bogotá, 2014.[16] A. V. Faminskii. The Cauchy problem for the Zakharov–Kuznetsov equation. Differentsial’nye Uravne niya, 31(6):1070–1081, 1995.[17] G. Fonseca, F. Linares, and G. Ponce. The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces. In Annales de l’Institut Henri Poincare (C) Non Linear Analysis, volume 30, pages 763–790. Elsevier, 2013[18] G. Fonseca and G. Ponce. The IVP for the Benjamin–Ono equation in weighted Sobolev spaces. Journal of Functional Analysis, 260(2):436 – 459, 2011.[19] S. V. Francis Ribaud. Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation. Discrete and Continuous Dynamical Systems, 37(1):449–483, 2017.[20] L. Grafakos. Classical fourier analysis, volume 2. Springer, 2008.[21] A. Grünrock and S. Herr. The Fourier restriction norm method for the Zakharov-Kuznetsov equation. arXiv preprint arXiv:1302.2034, 2013.[22] E. Hille. Methods in classical and functional analysis. 1972.[23] A. D. Ionescu and C. E. Kenig. Local and global well-posedness of periodic KP-I equations. Mathema tical Aspects of Nonlinear Dispersive Equations. Ann. Math. Stud, 163:181–211, 2009.[24] J. R. J. Iorio and W. V. L. Nunes. Introducao as equacoes de evolucao nao lineares. Cnpq/Impa, Rio de Janeiro, 1991.[25] R. J. Iório. KdV, BO and friends in weighted Sobolev spaces. In Functional-analytic methods for partial differential equations, pages 104–121. Springer, 1990.[26] I. J. Iorio Jr, R. J. Iorio Jr, and V. de Magalhães Iorio. Fourier analysis and partial differential equations, volume 70. Cambridge University Press, 2001.[27] R. José Iório, Jr. On the Cauchy problem for the Benjamin-Ono equation. Communications in partial differential equations, 11(10):1031–1081, 1986.[28] T. Kato. Quasi-linear equations of evolution, with applications to partial differential equations. Spectral theory and differential equations, pages 25–70, 1975. 118 Bibliografía[29] T. Kato. On the Cauchy problem for the (generalized) Korteweg-de Vries equation. Studies in applied mathematics, 8:93–128, 1983.[30] T. Kato and G. Ponce. Commutator estimates and the Euler and Navier-Stokes equations. Communi cations on Pure and Applied Mathematics, 41(7):891–907, 1988.[31] G. Keiser. Optical fiber communications. Wiley Online Library, 2003.[32] C. E. Kenig. On the local and global well-posedness theory for the KP-I equation. In Annales de l’Institut Henri Poincare (C) Non Linear Analysis, volume 21, pages 827–838. Elsevier, 2004.[33] C. E. Kenig, G. Ponce, and L. Vega. Well-posedness and scattering results for the generalized korteweg de vries equation via the contraction principle. Communications on Pure and Applied Mathematics, 46(4):527–620, 1993.[34] C. E. Kenig, G. Ponce, and L. Vega. A bilinear estimate with applications to the KdV equation. Journal of the American Mathematical Society, 9(2):573–603, 1996.[35] C. E. Kenig, G. Ponce, and L. Vega. On the unique continuation of solutions to the generalized KdV equation. Mathematical Research Letters, 10(5/6):833–846, 2003.[36] S. Kinoshita and R. Schippa. Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation. Journal of Functional Analysis, 280(6):108904, 2021.[37] H. Koch and N. Tzvetkov. On the local well-posedness of the Benjamin-Ono equation in Hs(R). 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El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro

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