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

Mohamad Darwich

doi:10.3934/dcdsb.2020087

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2020, Volume 25, Issue 9: 3715-3724. Doi: 10.3934/dcdsb.2020087

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

Mohamad Darwich

Mathematics Departement, Lebanese University, Hadat-Lebanon

Received: February 28, 2019

Revised: September 30, 2019

Early access: April 2020

Published: September 2020

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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) $.

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Mathematics Subject Classification: primary: 35A01, 35Q53; secondary: 35Q60.

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