Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 246, Issue 3, Pages 929-963Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2008.04.014
Keywords
Higher-order Camassa-Holm equation; Weak solutions; Existence Uniqueness; Geometric interpretation
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Funding
- Research Council of Norway
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We consider higher-order Camassa-Holm equations describing exponential curves of the manifold of smooth orientation-preserving diffeomorphisms of the unit circle in the plane. We establish the existence of global weak solutions. We also present some invariant spaces under the action of the equation. Moreover, we prove a weak equals strong uniqueness result. (C) 2008 Elsevier Inc. All rights reserved.
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