Uniformly attracting limit sets for the critically dissipative SQG equation

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