Well-posedness and weak rotation limit for the Ostrovsky equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Tsugawa, Kotaro

关键词: Ostrovsky equation;    KdV equation;    Well-posedness;    Cauchy problem;    Fourier restriction norm;    Low regularity;    Weak rotation limit;   

DOI  :  10.1016/j.jde.2009.09.009

来源: Elsevier

【 摘 要 】

We consider the Cauchy problem of the Ostrovsky equation. We first prove the time local well-posedness in the anisotropic Sobolev space H(s,a) with s > -a/2 - 3/4 and 0 <= a <= -1 by the Fourier restriction norm method. This result include the time local well-posedness in H(s) with s > -3/4 for both positive and negative dissipation. namely for both beta gamma > 0 and beta gamma < 0. We next consider the weak rotation limit. We prove that the solution of the Ostrovsky equation converges to the solution of the KdV equation when the rotation parameter gamma goes to 0 and the initial data of the KdV equation is in L(2). To show this result, we prove a bilinear estimate which is uniform with respect to gamma. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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