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Transactions of the American Mathematical Society

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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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Additional Information

Xinyu Mei
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Email: meixy13@lzu.edu.cn

Anton Savostianov
Affiliation: Department of Mathematics, Uppsala University, Uppsala 75106, Sweden
Email: anton.savostianov@math.uu.se

Chunyou Sun
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
Email: sunchy@lzu.edu.cn

Sergey Zelik
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China; Department of Mathematics, University of Surrey, Guildford GU2 7XH, United Kingdom
Email: s.zelik@surrey.ac.uk

DOI: https://doi.org/10.1090/tran/8317
Keywords: Damped wave equation, fractional damping, global attractor, unbounded domain, Strichartz estimates
Received by editor(s): April 30, 2020
Published electronically: March 2, 2021
Additional Notes: This work was partially supported by the RSF grant 19-71-30004 as well as the EPSRC grant EP/P024920/1 and NSFC grants No. 11471148, 11522109, 11871169.
Article copyright: © Copyright 2021 American Mathematical Society