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• W3103152671 endingPage "141" @default.
• W3103152671 startingPage "93" @default.
• W3103152671 abstract "We prove the existence of a compact global attractor for the dynamics of the forced critical surface quasi-geostrophic equation (SQG) and prove that it has finite fractal (box-counting) dimension. In order to do so we give a new proof of global regularity for critical SQG. The main ingredient is the nonlinear maximum principle in the form of a nonlinear lower bound on the fractional Laplacian, which is used to bootstrap the regularity directly from L ∞ to C α, without the use of De Giorgi techniques. We prove that for large time, the norm of the solution measured in a sufficiently strong topology becomes bounded with bounds that depend solely on norms of the force, which is assumed to belong merely to L ∞ ∩ H 1. Using the fact that the solution is bounded independently of the initial data after a transient time, in spaces conferring enough regularity, we prove the existence of a compact absorbing set for the dynamics in H 1, obtain the compactness of the linearization and the continuous differentiability of the solution map. We then prove exponential decay of high yet finite dimensional volume elements in H 1 along solution trajectories, and use this property to bound the dimension of the global attractor." @default.
• W3103152671 created "2020-11-23" @default.
• W3103152671 creator A5011148945 @default.
• W3103152671 creator A5037968657 @default.
• W3103152671 creator A5089255575 @default.
• W3103152671 date "2014-08-09" @default.
• W3103152671 modified "2023-10-02" @default.
• W3103152671 title "Long Time Dynamics of Forced Critical SQG" @default.
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