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
MathSciNet review:
4237944
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Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
1060930
ORCID:
0000-0001-5581-8414
Email:
anton.savostianov@math.uu.se
Chunyou Sun
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People’s Republic of China
ORCID:
0000-0003-3770-7651
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
MR Author ID:
357918
Email:
s.zelik@surrey.ac.uk
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