Publications [#330293] of Alexander A. Kiselev

Papers Published

1. Kiselev, A, Nonlocal maximum principles for active scalars, Advances in Mathematics, vol. 227 no. 5 (August, 2011), pp. 1806-1826, Elsevier BV [doi]
   (last updated on 2026/02/08)

   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 introduced in Kiselev, Nazarov and Volberg (2007) [19], formulating a more general criterion and providing new applications. The most interesting application is finite time regularization of weak solutions in the supercritical regime. © 2011 Elsevier Inc.