Ill-posedness for the 2D viscous shallow water equations in the critical Besov spaces

Jinlu Li, Pingzhou Hong, Weipeng Zhu

In this paper, we prove that the 2D viscous shallow water equations is ill-posed in the critical Besov spaces $\B^{\frac2p-1}_{p,1}(\R^2)$ with $p>4$. Our proof mainly depends on t…