Existence and regularity of the global attractor for a weakly damped forced shallow water equation in H |
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| Authors: | Yongsheng Li Xingyu Yang |
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| Affiliation: | aDepartment of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, PR China |
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| Abstract: | In this paper we prove the existence of the global attractor for a weakly damped forced shallow water equation in  . Moreover, we show that the global attractor is actually compact in  . The main method is the combination of the energy equation, a suitable splitting of the solutions, and bilinear estimates in Bourgain spaces. |
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| Keywords: | Shallow water equation Global attractor Asymptotic smoothing effect Bourgain spaces Bilinear estimates |
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