Attractors for Damped Quintic Wave Equations in Bounded Domains

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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Correspondence to Varga Kalantarov.

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This work is partially supported by the Russian Ministry of Education and Science (contract no. 8502).

Communicated by Nader Masmoudi.

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Kalantarov, V., Savostianov, A. & Zelik, S. Attractors for Damped Quintic Wave Equations in Bounded Domains. Ann. Henri Poincaré 17, 2555–2584 (2016). https://doi.org/10.1007/s00023-016-0480-y

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Keywords

  • Global Attractor
  • Galerkin Approximation
  • Strichartz Estimate
  • Asymptotic Compactness
  • Global Solvability