The Cauchy problem for the L2–critical generalized Zakharov-Kuznetsov equation in dimension 3

DOI10.1080/03605302.2021.1888119zbMath1477.35221arXiv2005.12482OpenAlexW3134877898MaRDI QIDQ5012778

João Pedro Ramos, Felipe Linares

Publication date: 25 November 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.12482

zbMATH Keywords

well-posednesslow regularityZakharov-Kuznetsov equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Local well-posedness for a fractional KdV-type equation ⋮ Convergence problem of the Kawahara equation on the real line ⋮ Convergence problem of Schrödinger equation and wave equation in low regularity spaces

Cites Work

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• Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons
• The Fourier restriction norm method for the Zakharov-Kuznetsov equation
• From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
• A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations
• A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results
• Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation
• A remark on the modified Zakharov-Kuznetsov equation in three space dimensions
• Nonlinear Schrödinger equations and sharp interpolation estimates
• The Cauchy problem for the 3D Zakharov-Kuznetsov equation
• Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
• Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation
• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
• Talbot effect for the cubic non-linear Schröedinger equation on the torus
• The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
• Global Smoothing for the Periodic KdV Evolution
• Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation
• Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation
• The initial-value problem for the Korteweg-de Vries equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Stability and instability of some nonlinear dispersive solitary waves in higher dimension
• Pointwise Convergence of the Schrödinger Flow
• Maximal Function Estimates and Local Well-Posedness for the Generalized Zakharov--Kuznetsov Equation
• Growth of Solutions to NLS on Irrational Tori
• Introduction to nonlinear dispersive equations
• Maximal functions associated to filtrations

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