Publications [#330294] of Alexander A. Kiselev

Papers Published

1. Kiselev, A; Nazarov, F, Variation on a theme of caffarelli and vasseur, Journal of Mathematical Sciences, vol. 166 no. 1 (March, 2010), pp. 31-39, Springer Nature [doi]
   (last updated on 2026/01/18)

   Abstract:
   Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur have shown that a certain class of weak solutions to the drift diffusion equation with initial data in L² gain Ḧolder continuity, provided that the BMO norm of the drift velocity is bounded uniformly in time. We show a related result: a uniform bound on the BMO norm of a smooth velocity implies a uniform bound on the C^β norm of the solution for some β > 0. We apply elementary tools involving the control of Ḧolder norms by using test functions. In particular, our approach offers a third proof of the global regularity for the critical surface quasigeostrophic (SQG) equation in addition to the two proofs obtained earlier. Bibliography: 6 titles. © 2010 Springer Science+Business Media, Inc.