Critical SQG in bounded domains
Peter Constantin, Mihaela Ignatova
TL;DR
This paper establishes global regularity results for the critical dissipative SQG equation in bounded domains, demonstrating interior Hölder and Lipschitz bounds for solutions with large initial data.
Contribution
It proves the first global a priori interior regularity bounds for the critical SQG equation in bounded domains with large data.
Findings
Global interior $C^{eta}$ bounds for large data
Lipschitz regularity of solutions
Applicability to bounded domains with Dirichlet Laplacian dissipation
Abstract
We consider the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove global a priori interior and Lipschitz bounds for large data.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Navier-Stokes equation solutions · Stability and Controllability of Differential Equations