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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Hirayama, Hiroyuki¹ 

[1] Univ Miyazaki, Org Promot Tenure Track, Miyazaki 8892192, Japan

关键词: Zakharov-Kuznetsov equation;    Burgers equation;    Well-posedness;    Cauchy problem;    Fourier restriction norm;   

DOI  :  10.1016/j.jde.2019.04.030

来源: Elsevier

【 摘 要 】

In the present paper, we consider the Cauchy problem of the 2D Zakharov-Kuznetsov-Burgers (ZKB) equation, which has the dissipative term -partial derivative(2)(x)u. This is known that the 2D Zakharov-Kuznetsov equation is well-posed in H-s (R-2) for s > 1/2, and the 2D nonlinear parabolic equation with quadratic derivative nonlinearity is well-posed in H-s (R-2) for s >= 0. By using the Fourier restriction norm with dissipative effect, we prove the well-posedness for ZKB equation in H-s (R-2) for s > -1/2. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free