NDLI: Continuity and analyticity for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs

Content Provider	Springer Nature Link
Author	Zhou, Shouming
Copyright Year	2016
Abstract	In this paper, we mainly study the well-posedness in the sense of Hadamard, non-uniform dependence, Hölder continuity and analyticity of the data-to-solution map for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs on both the periodic and the nonperiodic case. Using a Galerkin-type approximation scheme, it is shown that this equation is well-posed in Sobolev spaces $$H^{s} \times H^{s},s>5/2$$ in the sense of Hadamard, that is, the data-to-solution mapis continuous. In conjunction with the well-posedness estimate, it is also proved that this dependence is sharp by showing that the solution map is not uniformly continuous. Furthermore, the Hölder continuous in the $$H^r \times H^r$$ topology when $$0\le r< s$$ with Hölder exponent $$\alpha $$ depending on both s and r are shown. Finally, applying generalized Ovsyannikov type theorem and the basic properties of Sobolev-Gevrey spaces, we prove the Gevrey regularity and analyticity of the CCCH system. Moreover, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map
Ending Page	238
Page Count	44
Starting Page	195
File Format	PDF
ISSN	00269255
e-ISSN	14365081
Journal	Monatshefte für Mathematik
Issue Number	1
Volume Number	182
Language	English
Publisher	Springer Vienna
Publisher Date	2016-05-26
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cross-coupled Camassa-Holm Wave equation Analyticity Non-uniform dependence Gevrey regularity Mathematics Hölder continuity Initial value problems for nonlinear higher-order equations
Content Type	Text
Resource Type	Article
Subject	Mathematics

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