Well-posedness of higher-order Camassa-Holm equations

作者：Coclite G M^*; Holden H; Kadsen K H

来源：Journal of Differential Equations, 2009, 246(3): 929-963.

DOI：10.1016/j.jde.2008.04.014

• Higher-order Camassa-Holm equation
• Weak solutions
• Existence Uniqueness
• Geometric interpretation

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.

• 出版日期2009-2-1