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 language | English (US) |
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Article number | 298 |
Pages (from-to) | 298-318 |
Number of pages | 21 |
Journal | Nonlinearity |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - Jan 13 2016 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
Keywords
- De Giorgi
- global attractor
- nonlinear maximum principle
- surface quasi-geostrophic equation