## Differential and Integral Equations

### 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.

#### Article information

Source
Differential Integral Equations Volume 29, Number 3/4 (2016), 241-268.

Dates
First available in Project Euclid: 18 February 2016

Fan, Lili; Gao, Hongjun. Local well-posedness and persistence properties for the variable depth KDV general equations in Besov space $B^{ \frac 32 }_{2,1}$. Differential Integral Equations 29 (2016), no. 3/4, 241--268.https://projecteuclid.org/euclid.die/1455806024