On the periodic Zakharov-Kuznetsov equation

DOI10.3934/dcds.2019145zbMath1420.35319arXiv1809.02027OpenAlexW2891474836WikidataQ128231222 ScholiaQ128231222MaRDI QIDQ2423634

Mahendra Panthee, Tristan Robert, Nickolay Tzvetkov, Felipe Linares

Publication date: 20 June 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02027

zbMATH Keywords

well-posednessStrichartz estimatedispersive equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (8)

Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows ⋮ On the properties in solutions of the Shrira equation ⋮ On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations ⋮ The IVP for a periodic generalized ZK equation ⋮ Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus ⋮ Unnamed Item ⋮ Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation ⋮ Periodic Cauchy problem for one two-dimensional generalization of the Benjamin-Ono equation in Sobolev spaces of low regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Fourier restriction norm method for the Zakharov-Kuznetsov equation
• Global well-posedness of the KP-I initial-value problem in the energy space
• The Cauchy problem for the 3D Zakharov-Kuznetsov equation
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
• Remark on the semilinear ill-posedness for a periodic higher-order KP-I equation
• On the local and global well-posedness theory for the KP-I equation
• On the Cauchy problem for the periodic fifth-order KP-I equation.
• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
• On finite energy solutions of the KP-I equation
• The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
• Well-Posedness Results for the Three-Dimensional Zakharov--Kuznetsov Equation
• Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation
• Commutator estimates and the euler and navier-stokes equations
• 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
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Well-Posedness for the ZK Equation in a Cylinder and on the Background of a KdV Soliton
• Well-posedness for the fifth-order KdV equation in the energy space
• Introduction to nonlinear dispersive equations

This page was built for publication: On the periodic Zakharov-Kuznetsov equation