Some properties for the fifth‐order Camassa‐Holm type equation.

In this paper, we study several problems of the fifth‐order Camassa‐Holm type (FOCHT) equation. The local well‐posedness and blow‐up scenario are established at first. Then we prove the global existence under some conditions and analyze the large‐time behavior of the support of momentum density. Finally, we discuss the persistence property in Sobolev space. [ABSTRACT FROM AUTHOR]