Local rigidity of certain solvable group actions on tori
Xinyu Mei 1, , Yangmin Xiong 2, and Chunyou Sun 2,,
School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong, China, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, Guangdong, China
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China
Corresponding author: Chunyou Sun, sunchy@lzu.edu.cn
Received January 2020 Revised May 2020 Published July 2020
Fund Project: This work was partly supported by the NSFC Grants 11471148, 11522109 and 11871169
In this paper, the non-autonomous dynamical behavior of weakly damped wave equation with a sup-cubic nonlinearity is considered in locally uniform spaces. We first prove the global well-posedness of the Shatah-Struwe solutions, then establish the existence of the $ \big(H_{lu}^{1}(\mathbb{R}^{3})\times L_{lu}^{2}(\mathbb{R}^{3}),H_{\rho}^{1}(\mathbb{R}^{3})\times L_{\rho}^{2}(\mathbb{R}^{3})\big) $-pullback attractor for the Shatah-Struwe solutions process of this equation. The results are based on the recent extension of Strichartz estimates for the bounded domains.
Keywords: Wave equation, Locally uniform spaces, Shatah-Struwe solution, Pullback attractor.
Mathematics Subject Classification: Primary:35B41, 35Q55, 35Q56, 37L40, 76F20.
Citation: Xinyu Mei, Yangmin Xiong, Chunyou Sun. Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 569-600. doi: 10.3934/dcds.2020270
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Xinyu Mei Yangmin Xiong Chunyou Sun