The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the so-called Shatah-Struwe solutions, their dissipativity, the existence of a locally compact global attractors (in the uniformly local phase spaces) and their extra regularity.

中文翻译：

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$\mathbb {R}^3$中弱阻尼五次波动方程的无限能量解

该论文全面研究了 $\mathbb{R}^3$ 中具有五次非线性的半线性弱阻尼波动方程的无限能量解及其长期行为。这项研究包括所谓的 Shatah-Struwe 解的全局适定性、它们的耗散性、局部紧凑全局吸引子的存在（在均匀局部相空间中）及其额外的规律性。