Ill-posedness and global solution for the $b$-equation

Yingying Guo, Weikui Ye

In this paper, we consider the Cauchy problem for the $b$-equation. Firstly, for $s>\frac{3}{2},$ if $u_0(x)\in H^s(\mathbb{R})$ and $m_{0}(x)=u_{0}(x)-u_{0xx}(x)\in L^{1}(\mathbb{…