Strong attractors for weakly damped quintic wave equation in bounded domains

Senlin Yan; Zhijun Tang; Chengkui Zhong

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arXiv · 2206.03158

Strong attractors for weakly damped quintic wave equation in bounded domains

Senlin Yan·Zhijun Tang·Chengkui Zhong

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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 $\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(\Omega)\cap H^1_0(\Omega)\times H^1_0(\Omega)$. Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.

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Senlin Yan, Zhijun Tang, Chengkui Zhong. 2022-06-07. Strong attractors for weakly damped quintic wave equation in bounded domains. https://arxiv.org/abs/2206.03158

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