Abstract
In this paper, we consider the Cauchy problem of the long-wave–short-wave resonance equations. By making use of a Strichartz-type inequality for the solutions, decomposing suitably the solution semigroup into a decay parts and a more regular parts, and ruling out the “vanishing” and “dichotomy” of the solutions, we prove the existence of the global attractor and the asymptotic smoothing effect of the solutions.
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