Attractor For The Semi-dissipative 2D Boussinesq Equations With Stress-free Boundary Conditions

In this paper,we study the long-term behavior of a partially dissipative 2D Boussi-nesq system under stress-free boundary conditions.First,we review the existence and uniqueness of the solution.Next,we prove that the solution of the equation is dissi-pative in H2,and we study the properties and structural characteristics of the attractor of the system ?.Since the velocity variable u is dissipative in H2,according to the Sobolev embedding theorem,we obtain that the attraction of the weak ?-attractor with respect to u is in the strong topology of V.