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|Abstract:||We obtain a family of nonlinear maximum principles for linear dissipa- tive 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 dissi- pative 2D Boussinesq equations.|
|Electronic Publication Date:||31-Aug-2012|
|Citation:||Constantin, Peter, Vicol, Vlad. (2012). Nonlinear maximum principles for dissipative linear nonlocal operators and applications. GEOMETRIC AND FUNCTIONAL ANALYSIS, 22 (1289 - 1321. doi:10.1007/s00039-012-0172-9|
|Pages:||1289 - 1321|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||GEOMETRIC AND FUNCTIONAL ANALYSIS|
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