Long time behavior of solutions of Davey-Stewartson equations

Abstract

In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator inLp (Ω) and prove that the Davey-Stewartson system possesses a compact global attractorAp inLP (Ω). Furthermore, one show that the attractor is in fact independent ofp and prove the attractor has finite Hausdorff and fractal dimensions.