Well posedness for a higher order modified Camassa-Holm equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Olson, Erika A.

关键词: Modified Camassa-Holm equation;    Nonlinear dispersive equations;    Harmonic analysis;    Bilinear estimates;    Well posedness;    Cauchy problem;    Sobolev spaces;   

DOI  :  10.1016/j.jde.2008.12.001

来源: Elsevier

【 摘 要 】

We show that the Cauchy problem for a higher order modification of the Cannassa-Holm equation is locally well posed for initial data in the Sobolev space H(s)(R) for s > s', where 1/4 <= s' < 1/2 and the value of s' depends on the order of equation. Employing harmonic analysis methods we derive the corresponding bilinear estimate and then use a contraction mapping argument to prove existence and uniqueness of solutions. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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