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Geometric and Functional Analysis

, Volume 22, Issue 5, pp 1289–1321 | Cite as

Nonlinear maximum principles for dissipative linear nonlocal operators and applications

  • Peter Constantin
  • Vlad Vicol
Article

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 and phrases

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

Mathamatical Subject Classification (2000)

35Q35 76B03 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsThe University of ChicagoChicagoUSA

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