Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space

Abstract

In the present paper, we consider the Cauchy problem of the 2D Zakharov-Kuznetsov-Burgers (ZKB) equation, which has the dissipative term $-{\partial }_x^{2}u$. This is known that the 2D Zakharov-Kuznetsov equation is well-posed in $H^s({\mathbb{R}}^2)$ for $s>1/2$, and the 2D nonlinear parabolic equation with quadratic derivative nonlinearity is well-posed in $H^s({\mathbb{R}}^2)$ for $s\ge 0$. By using the Fourier restriction norm with dissipative effect, we prove the well-posedness for ZKB equation in $H^s({\mathbb{R}}^2)$ for $s>-1/2$.

25 pages

References in corpus (2)

• The Fourier restriction norm method for the Zakharov-Kuznetsov equation
• On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation

Cited by in corpus (1)

• Optimal Decay Estimate and Asymptotic Profile for Solutions to the Generalized Zakharov-Kuznetsov-Burgers Equation in 2D