Local well-posedness and blow-up of solutions for wave equations on shallow water with periodic depth
oleh: Lili Fan, Hongjun Gao
| Format: | Article |
|---|---|
| Diterbitkan: | Texas State University 2015-01-01 |
Deskripsi
In this article, we consider a nonlinear evolution equation for surface waves in shallow water over periodic uneven bottom. The local well-posedness in Sobolev space $H^s(\mathbb{S})$ with $s>3/2$ is established by applying Kato's theory. Then a blow up criterion is determined in $H^s(\mathbb{S})$, $s>3/2$. Finally, some blow-up results are given for a simplified model.