Continuity properties of the solution map for the generalized reduced Ostrovsky equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Davidson, Melissa

关键词: Generalized reduced Ostrovsky equation;    Ostrovsky equation;    Short pulse equation;    Vakhnenko equation;    Cauchy problem;    Sobolev spaces;    Well-posedness;    Nonuniform dependence on initial data;    Approximate solutions;    Holder continuity;   

DOI  :  10.1016/j.jde.2011.11.013

来源: Elsevier

【 摘 要 】

It is shown that the data-to-solution map for the generalized reduced Ostrovsky (gRO) equation is not uniformly continuous on bounded sets in Sobolev spaces on the circle with exponent s > 3/2. Considering that for this range of exponents the gRO equation is well posed with continuous dependence on initial data, this result makes the continuity of the solution map an optimal property. However, if a weaker H-r-topology is used then it is shown that the solution map becomes Holder continuous in H-s. (C) 2011 Elsevier Inc. All rights reserved.

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