Global attractor of the fractional damping wave equation on ℝ3. Issue 2 (22nd January 2022) - Guo, Yantao; Ding, Pengyan
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 ) .