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arXiv · 1009.0542

Nonlocal maximum principles for active scalars

Alexander Kiselev
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Abstract

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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Alexander Kiselev. 2010-09-02. Nonlocal maximum principles for active scalars. https://arxiv.org/abs/1009.0542

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