Global wellposedness of cubic Camassa-Holm equations

Qingtian Zhang (1)

1 Department of Mathematics, Penn State University

In this paper, we study the Cauchy problem of cubic Camassa-Holm equation or so-called Fokas-Olver-Rosenau-Qiao equation. This equation is derived from a model of shallow water dynamics. We prove the global existence of entropy weak solution to this problem in space H 1 ∩ ˙ W 2,1. The stability and uniqueness of entropy weak solution are obtained in W 1,1 .

Domaines: Equations aux dérivées partielles [math.AP]

Qingtian Zhang. Global wellposedness of cubic Camassa-Holm equations. 2015. ⟨hal-01213780⟩