Infinite energy solutions for weakly damped quintic wave equations in ℝ³

Mei, Xinyu; Savostianov, Anton; Sun, Chunyou; Zelik, Sergey

doi:10.1090/tran/8317

Infinite energy solutions for weakly damped quintic wave equations in $\mathbb{R}^3$

Authors: Xinyu Mei, Anton Savostianov, Chunyou Sun and Sergey Zelik
Journal: Trans. Amer. Math. Soc. 374 (2021), 3093-3129
MSC (2020): Primary 35B40, 35B45, 35L70
DOI: https://doi.org/10.1090/tran/8317
Published electronically: March 2, 2021
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Abstract: 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.

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