# American Institute of Mathematical Sciences

September  2020, 25(9): 3715-3724. doi: 10.3934/dcdsb.2020087

## Local and global well-posedness in the energy space for the dissipative Zakharov-Kuznetsov equation in 3D

Received  March 2019 Revised  October 2019 Published  September 2020 Early access  April 2020

In this paper, we consider the Zakharov-Kuznetsov equation in 3D, with a dissipative term of order $0 < \alpha \leq 2$ in the $x$ direction. We prove that the problem is locally well-posed in $H^{s}( { I\!\!R}^3)$, for $s > 1-\frac{\alpha}{2}$, and by an a priori energy estimate, we prove that the problem is globally well-posed in $H^{1}( { I\!\!R}^3)$.

Citation: Mohamad Darwich. Local and global well-posedness in the energy space for the dissipative Zakharov-Kuznetsov equation in 3D. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3715-3724. doi: 10.3934/dcdsb.2020087
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