Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Peter Constantin, Vlad Vicol

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1289-1321
Number of pages33
JournalGeometric and Functional Analysis
Volume22
Issue number5
DOIs
StatePublished - Oct 1 2012

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Maximum Principle
Global Regularity
Operator
Incompressible Euler Equations
Boussinesq Equations
Antisymmetric
Burgers Equation
Fractional
Perturbation

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Cite this

Nonlinear maximum principles for dissipative linear nonlocal operators and applications. / Constantin, Peter; Vicol, Vlad.

In: Geometric and Functional Analysis, Vol. 22, No. 5, 01.10.2012, p. 1289-1321.

Research output: Contribution to journalArticle

Constantin, Peter ; Vicol, Vlad. / Nonlinear maximum principles for dissipative linear nonlocal operators and applications. In: Geometric and Functional Analysis. 2012 ; Vol. 22, No. 5. pp. 1289-1321.
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