Nonlinear maximum principles for dissipative linear nonlocal operators and applications

Peter Constantin, Vlad Vicol

Research output: Contribution to journalArticlepeer-review

213 Scopus citations


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
Issue number5
StatePublished - Oct 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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


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