A note on the initial value problem for a higher‐order Camassa–Holm equation

Abstract

AbstractConsidered herein is the Cauchy problem for a higher‐order Camassa–Holm equation. Based on the local well‐posedness results for this problem, the non‐uniformly continuous dependence on initial data is established in Sobolev spaces with on the line by using the method of approximate solutions. In the periodic case, the non‐uniformly continuous dependence on initial data in Besov spaces and are proved. Finally, the persistence property of solutions for this problem is studied.