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.
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