Ill-posedness for the 2D viscous shallow water equations in the critical Besov spaces (1712.09546v2)

Abstract: 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 the method introduced by the paper \cite{C-M-Z4}.