Nonlinear maximum principles for dissipative linear nonlocal operators and applications

被引：225
|
作者：
Constantin, Peter [1 ]
Vicol, Vlad [2 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2012年 / 22卷 / 05期
基金：
美国国家科学基金会;
关键词：
Nonlinear lower bound; maximum-principle; fractional Laplacian; anti-symmetrically forced Euler equations; nonlocal dissipation; GLOBAL WELL-POSEDNESS; EULER EQUATIONS; REGULARITY;
D O I：
10.1007/s00039-012-0172-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：1289 / 1321
页数：33
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