Uniformly attracting limit sets for the critically dissipative SQG equation

Peter Constantin; Michele Coti Zelati; Vlad Vicol

doi:10.1088/0951-7715/29/2/298

Uniformly attracting limit sets for the critically dissipative SQG equation

Peter Constantin, Michele Coti Zelati, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

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 H^1+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 language	English (US)
Article number	298
Pages (from-to)	298-318
Number of pages	21
Journal	Nonlinearity
Volume	29
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/29/2/298
State	Published - Jan 13 2016

Keywords

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

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/29/2/298

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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.",

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AU - Zelati, Michele Coti

AU - Vicol, Vlad

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N2 - 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.

AB - 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.

KW - De Giorgi

KW - global attractor

KW - nonlinear maximum principle

KW - surface quasi-geostrophic equation

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Uniformly attracting limit sets for the critically dissipative SQG equation

Abstract

Keywords

ASJC Scopus subject areas

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