Attractors for autonomous and nonautonomous 3D Benjamin–Bona–Mahony equations

Abstract

In this paper we consider the long time behavior of the three dimensional Benjamin–Bona–Mahony equations for the autonomous and nonautonomous cases. A useful decomposition method is introduced to overcome the difficulties in proving the asymptotical regularity of the 3D Benjamin–Bona–Mahony equations. For the autonomous case, we prove the existence of global attractor when the external forcing belongs to V′. For the nonautonomous case, we only assume that f(x, t) is translation bounded instead of translation compact. By means of this useful decomposition methods, we prove the asymptotic regularity of solutions of 3D Benjamin–Bona–Mahony equations and also obtain the existence of the uniform attractor.