Uniformly attracting limit sets for the critically dissipative SQG equation

作者：Constantin Peter^*; Zelati Michele Coti^*; Vicol Vlad^*

来源：Nonlinearity, 2016, 29(2): 298-318.

DOI：10.1088/0951-7715/29/2/298

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

We consider the global attractor of the critical surface quasi-geostrophic (SQG) semigroup S(t) on the scale-invariant space H-1(T-2). It was shown in [15] that this attractor is finite dimensional, and that it attracts uniformly bounded sets in H1+delta(T-2) for any delta > 0, leaving open the question of uniform attraction in H-1(T-2). In this paper we prove the uniform attraction in H-1(T-2), by combining ideas from the De Giorgi iteration and nonlinear maximum principles.

• 出版日期2016-2