Talk #1: Long time behavior of forced 2D SQG equations

Talk #1: Long time behavior of forced 2D SQG equations

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Peter Constantin, Princeton University
Rutgers - Hill Center, Room 525

We prove the absence of anomalous dissipation of energy for the forced critical surface quasi-geostrophic equation (SQG) in {\mathbb {R}}^2  and the existence of a compact finite dimensional golbal attractor in      {\mathbb T}^2. The absence of anomalous dissipation can be proved for rather rough forces, and employs methods that are suitable for situations when uniform bounds for the dissipation are not available. For the        finite dimensionality of the attractor in the space-periodic case, the global regularity of the forced critical SQG equation needs to be revisited, with a new and final proof. We show that the system looses infinite dimensional information, by obtaining strong long time bounds that are independent of initial data. This is joint work with A. Tarfulea and V. Vicol.