Annales Henri Poincaré

, Volume 17, Issue 9, pp 2555–2584 | Cite as

Attractors for Damped Quintic Wave Equations in Bounded Domains

  • Varga Kalantarov
  • Anton Savostianov
  • Sergey Zelik
Article

Abstract

The dissipative wave equation with a critical quintic non-linearity in smooth bounded three-dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Varga Kalantarov
    • 1
  • Anton Savostianov
    • 2
  • Sergey Zelik
    • 2
  1. 1.Department of MathematicsKoç UniversitySariyerTurkey
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUK

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