Global well-posedness for the 3D Zakharov-Kuznetsov equation in energy space \(H^1\)

DOI10.3934/DCDSS.2016075zbMath1353.35112OpenAlexW2553526753MaRDI QIDQ728085

Zhaohi Huo, Yueling Jia, Qiaoxin Li

Publication date: 22 December 2016

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

Full work available at URL: https://doi.org/10.3934/dcdss.2016075

zbMATH Keywords

well-posednessZakharov-Kuznetsov equationdyadic \(X_{s,b}\) spaces in higher dimension

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Cites Work

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• Global well-posedness of the KP-I initial-value problem in the energy space
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• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• 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
• Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A bilinear estimate with applications to the KdV equation

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