On the sharp local well-posedness for the modified Ostrovsky, Stepanyams and Tsimring equation
Esfahani A. Wang H.
August 2021Elsevier Ltd
Nonlinear Analysis: Real World Applications
2021#60
In this paper, we consider the modified Ostrovsky, Stepanyams and Tsimring equation ut+uxxx−η(Hux+Huxxx)+u2ux=0. We prove that the associated initial value problem is locally well-posed in Sobolev spaces Hs(R) for s>−1∕2. We also prove that our result is sharp in the sense that the flow map of this equation fails to be C3 in Hs(R) for s<−1∕2. Moreover, we prove that for any s>1∕2 and T>0, its solution converges in C([0,T];Hs(R)) to that of the mKdV equation if η tends to 0.
Cauchy problem , Inviscid limit , Local well-posedness , OST equation
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Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China
Department of Mathematics
School of Mathematics and Statistics
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