Local well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation
1 College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, P.R. China
2 School of Economics Management, Chongqing Normal University, Chongqing, 401331, P.R. China
Boundary Value Problems 2014, 2014:9 doi:10.1186/1687-2770-2014-9Published: 8 January 2014
This paper deals with the Cauchy problem for a generalized Camassa-Holm equation with high-order nonlinearities,
where and . This equation is a generalization of the famous equation of Camassa-Holm and the Novikov equation. The local well-posedness of strong solutions for this equation in Sobolev space with is obtained, and persistence properties of the strong solutions are studied. Furthermore, under appropriate hypotheses, the existence of its weak solutions in low order Sobolev space with is established.