Abstract
We obtain estimates near the boundary for the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove that global regularity up to the boundary holds if and only if a certain quantitative vanishing of the scalar at the boundary is maintained.
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The work of PC was partially supported by NSF Grant DMS-1209394
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Constantin, P., Ignatova, M. Estimates Near the Boundary for Critical SQG. Ann. PDE 6, 3 (2020). https://doi.org/10.1007/s40818-020-00079-7
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DOI: https://doi.org/10.1007/s40818-020-00079-7