Lili Fan, Hongjun Gao
Abstract:
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
with
is established by
applying Kato's theory. Then a blow up criterion is determined in
,
.
Finally, some blow-up results are given for
a simplified model.
Submitted September 24, 2014. Published January 5, 2015.
Math Subject Classifications: 35Q53, 35B30, 35G25, 35B44.
Key Words: Shallow water equation; variable depth; well-posedness; blow-up.
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Lili Fan School of Mathematical Science and Jiangsu Key Laboratory for NSLSCS Nanjing Normal University, Nanjing 210023, China email: fanlily89@126.com |
Hongjun Gao School of Mathematical Science and Jiangsu Key Laboratory for NSLSCS Nanjing Normal University, Nanjing 210023, China. email: gaohj@njnu.edu.cn |
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