Long time behavior for the weakly damped driven long-wave-short-wave resonance equations |
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Authors: | Yongsheng Li |
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Institution: | School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510640, PR China |
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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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Keywords: | 35Q55 37L50 |
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