Nonlocal maximum principles for active scalars

Details Nonlocal maximum principles for active scalars Nonlocal maximum principles for active scalars

2010-09-02

arxiv.org/abs/1009.0542v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations are 2D Euler, Burgers, and 2D surface quasi-geostrophic equations. Many questions about regularity and properties of solutions of these equations remain open. We develop the idea of nonlocal maximum principle, formulating a more general criterion and providing new applications. The most interesting application is finite time regularization of weak solutions in the supercritical regime.

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