The Study of Solution of Dissipative Camassa-Holm Equation on Total Space

Abstract

Abstract. The dissipative Camassa-Holm equation is an important fluid equation which has close relation to turbulent phenomenon. Dissipative CH equation can be expressed as ODE through Galerkin method.Using prior estimate we get the existence of global solution for dissi-pative CH equation on total space about time t. Through norm estimate we investigate properties of solution of dissipative CH equation,then we find that the dissipative CH equation possesses global attractor under condition and the equation also possesses peaked solution. Stationary so-lution is studied, meanwhile the existence and uniqueness of the stationary solution belonging to absorbing set are obtained.