Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Peter Constantin; Vlad Vicol

doi:10.1007/s00039-012-0172-9

Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Peter Constantin, Vlad Vicol

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

219 Scopus citations

Abstract

We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.

Original language	English (US)
Pages (from-to)	1289-1321
Number of pages	33
Journal	Geometric and Functional Analysis
Volume	22
Issue number	5
DOIs	https://doi.org/10.1007/s00039-012-0172-9
State	Published - Oct 2012

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Nonlinear lower bound
anti-symmetrically forced Euler equations
fractionalLaplacian
maximum-principle
nonlocal dissipation

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10.1007/s00039-012-0172-9

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abstract = "We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.",

keywords = "Nonlinear lower bound, anti-symmetrically forced Euler equations, fractionalLaplacian, maximum-principle, nonlocal dissipation",

author = "Peter Constantin and Vlad Vicol",

note = "Funding Information: PC{\textquoteright}s research was partially supported by NSF-DMS grant 0804380.",

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AU - Constantin, Peter

AU - Vicol, Vlad

N1 - Funding Information: PC’s research was partially supported by NSF-DMS grant 0804380.

PY - 2012/10

Y1 - 2012/10

N2 - We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.

AB - We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d-dimensional Burgers equations. In addition we give applications of the nonlinear maximum principle to the global regularity of a slightly dissipative anti-symmetric perturbation of 2D incompressible Euler equations and generalized fractional dissipative 2D Boussinesq equations.

KW - Nonlinear lower bound

KW - anti-symmetrically forced Euler equations

KW - fractionalLaplacian

KW - maximum-principle

KW - nonlocal dissipation

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

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ER -

Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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