Uniformly attracting limit sets for the critically dissipative SQG equation. (13th January 2016)

• Record Type: Journal Article
• Authors: Constantin, Peter; Zelati, Michele Coti; Vicol, Vlad
• Is Part Of: Nonlinearity. Volume 29:Number 2(2016:Feb.)
• Page Start: 298
• Page End: 318
• Publication Date: 2016-01-13
• Subjects: surface quasi-geostrophic equation -- nonlinear maximum principle -- De Giorgi -- global attractor; 35Q35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/2/298
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the global attractor of the critical surface quasi-geostrophic (SQG) semigroup S ( t ) on the scale-invariant space . It was shown in [015 ] that this attractor is finite dimensional, and that it attracts uniformly bounded sets in for any, leaving open the question of uniform attraction in . In this paper we prove the uniform attraction in, by combining ideas from the De Giorgi iteration and nonlinear maximum principles.