Local well-posedness and persistence properties for the variable depth KDV general equations in Besov space $B^{ \frac 32 }_{2,1}$

Abstract

In this paper, we consider a nonlinear evolution equation for surface waves in shallow water over uneven bottom. First, the local well-posedness is obtained in Besov space $B^{ \frac 32 }_{2,1}$. Then, persistence properties on strong solutions are also investigated.