The Cauchy Problem for the Shallow Water Type Equations in Low Regularity Spaces on the Circle
Host
Department of Applied Mathematics
Speaker
Wei Yan
School of Mathematics and Information Science, Henan Normal University
http://www.htu.cn/math/2011/1103/c1204a28073/page.htm
Description
In this paper, we investigate the Cauchy problem for the shallow water type equation $$u_{t} + u_{xxx} + \frac{1}{2}(u^{2})_{x}+\partial_{x}(1−\partial_{x} ^{2}) ^{-1}\left(u^{2}+\frac{1}{2}(u^{2})_{x}\right)=0,\quad x\in T=R/2πλ$$ with low regularity data in the periodic settings and \(\lambda≥\). We prove that the bilinear estimate in \(X_{s,b}\) with \(s<1/2\) is invalid. We also prove that the problem is locally wellposed in \(H^{s}(T)\) with \(1/6
Event Topic
Stochastic & Multiscale Modeling and Computation