WELL-POSEDNESS OF HIGHER-ORDER CAMASSA-HOLM EQUATIONS

Coclite, Giuseppe M.; Holden, Helge; Karlsen, Kenneth H.
Research report
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Year
2006
Permanent link
http://urn.nb.no/URN:NBN:no-23542

Is part of
Preprint series. Pure mathematics
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Abstract
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 a strongly continuous semigroup of global weak solutions. We also present some invariant spaces under the action of that semigroup. Moreover, we prove a "weak equals strong" uniqueness result.