Uniformly attracting limit sets for the critically dissipative SQG equation

Peter Constantin, Michele Coti Zelati, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We consider the global attractor of the critical surface quasi-geostrophic (SQG) semigroup S(t) on the scale-invariant space H1(double-struck T2). It was shown in [15] that this attractor is finite dimensional, and that it attracts uniformly bounded sets in H1+δ(double-struck T2) for any δ > 0, leaving open the question of uniform attraction in H1(double-struck T2). In this paper we prove the uniform attraction in H1(double-struck T2), by combining ideas from the De Giorgi iteration and nonlinear maximum principles.

Original languageEnglish (US)
Article number298
Pages (from-to)298-318
Number of pages21
JournalNonlinearity
Volume29
Issue number2
DOIs
StatePublished - Jan 13 2016

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Quasi-geostrophic Equations
Maximum principle
Limit Set
attraction
maximum principle
Scale Invariant
Bounded Set
Global Attractor
Maximum Principle
iteration
Attractor
Semigroup
Iteration

Keywords

  • De Giorgi
  • global attractor
  • nonlinear maximum principle
  • surface quasi-geostrophic equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Uniformly attracting limit sets for the critically dissipative SQG equation. / Constantin, Peter; Zelati, Michele Coti; Vicol, Vlad.

In: Nonlinearity, Vol. 29, No. 2, 298, 13.01.2016, p. 298-318.

Research output: Contribution to journalArticle

Constantin, Peter ; Zelati, Michele Coti ; Vicol, Vlad. / Uniformly attracting limit sets for the critically dissipative SQG equation. In: Nonlinearity. 2016 ; Vol. 29, No. 2. pp. 298-318.
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