In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.
This paper studies the long time behavior of the following Cauchy problem δu/δt＋σδ^4u/δx^4＋ru＋uδu/δx=f,x∈R,t〉0,The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.
