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

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