Global attractor of the fractional damping wave equation on ℝ3. Issue 2 (22nd January 2022)

• Record Type: Journal Article
• Authors: Guo, Yantao; Ding, Pengyan
• Is Part Of: Applicable analysis. Volume 101:Issue 2(2022)
• Page Start: 592
• Page End: 604
• Publication Date: 2022-01-22
• Subjects: Wave equation -- dynamic system -- fractional damping -- global attractor; Primary: 35B40 -- 35B41 -- Secondary: 35B65 -- 37L30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1757075
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The paper studies the well-posedness and the longtime behaviors of the fractional damping wave equation on R 3 with critical nonlinearity, we firstly prove the well-posedness of weak solutions via an established Strichartz estimate; Secondly, by the uniformly tail estimate and the energy identity, we prove that the corresponding semigroup possesses a global attractor in the energy space H 1 ( R 3 ) × L 2 ( R 3 ) .