Abstract
In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of R3. Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space H2(Ω)∩H01(Ω)×H01(Ω). Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.
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