Global regularity for critical SQG in bounded domains

Peter Constantin; Mihaela Ignatova; Quoc Hung Nguyen

doi:10.1002/cpa.22221

Global regularity for critical SQG in bounded domains

Peter Constantin, Mihaela Ignatova, Quoc Hung Nguyen

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

Abstract

We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in (Formula presented.). We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.

Original language	English (US)
Pages (from-to)	3-59
Number of pages	57
Journal	Communications on Pure and Applied Mathematics
Volume	78
Issue number	1
DOIs	https://doi.org/10.1002/cpa.22221
State	Published - Jan 2025

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.22221

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title = "Global regularity for critical SQG in bounded domains",

abstract = "We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in (Formula presented.). We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.",

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AU - Nguyen, Quoc Hung

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AB - We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in (Formula presented.). We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.

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Global regularity for critical SQG in bounded domains

Abstract

All Science Journal Classification (ASJC) codes

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