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

TL;DR

This paper demonstrates that the 2D viscous shallow water equations are ill-posed in certain critical Besov spaces for p>4, highlighting limitations of well-posedness in these functional settings.

Contribution

It establishes ill-posedness of the 2D viscous shallow water equations in specific Besov spaces, extending understanding of their mathematical behavior.

Findings

Ill-posedness in critical Besov spaces for p>4

Utilizes method from previous work 

Highlights limitations of solution regularity

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}.