Estimates Near the Boundary for Critical SQG

Peter Constantin; Mihaela Ignatova

doi:10.1007/s40818-020-00079-7

Estimates Near the Boundary for Critical SQG

Peter Constantin, Mihaela Ignatova

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Article number	3
Journal	Annals of PDE
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/s40818-020-00079-7
State	Published - Jun 1 2020

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Geometry and Topology
Mathematical Physics
Physics and Astronomy(all)

Keywords

Bounded domains
Estimates near the boundary
Global regularity
SQG

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10.1007/s40818-020-00079-7

Cite this

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title = "Estimates Near the Boundary for Critical SQG",

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.",

keywords = "Bounded domains, Estimates near the boundary, Global regularity, SQG",

author = "Peter Constantin and Mihaela Ignatova",

note = "Funding Information: The work of PC was partially supported by NSF Grant DMS-1209394 Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

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AU - Ignatova, Mihaela

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AB - 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.

KW - Bounded domains

KW - Estimates near the boundary

KW - Global regularity

KW - SQG

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JO - Annals of PDE

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Estimates Near the Boundary for Critical SQG

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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