Global attractor for the regularized Bénard problem

Abstract

In this paper, we study the asymptotic behaviour of weak solutions for the regularized Bénard problem. We establish the global existence and uniqueness of weak solutions of this problem and give a proof for the existence of global attractor in the three-dimensional case for this system.

Keywords:

• Bénard problem
• global attractor
• weak solutions

AMS Subject Classifications:

• 35D05
• 76D03