Nonlinear maximum principles for dissipative linear nonlocal operators and applications

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 a...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 22; no. 5; pp. 1289 - 1321
Main Authors Constantin, Peter, Vicol, Vlad
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.10.2012
Subjects
Analysis
Mathematics
Mathematics and Statistics
anti-symmetrically forced Euler equations
nonlocal dissipation
maximum-principle
35Q35
76B03
Nonlinear lower bound
fractionalLaplacian
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Summary: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.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-012-0172-9