We consider higher-order Camassa–Holme quations 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.
Well-posedness of higher-order Camassa–Holm equations / Coclite, Giuseppe Maria; Holden, H; Karlsen, K. H.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 246:3(2009), pp. 929-963. [10.1016/j.jde.2008.04.014]
Well-posedness of higher-order Camassa–Holm equations
COCLITE, Giuseppe Maria;
2009-01-01
Abstract
We consider higher-order Camassa–Holme quations 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.File in questo prodotto:
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