A profile decomposition approach to the L-t(infinity)(L-x(3)) Navier-Stokes regularity criterion

作者：Gallagher Isabelle^*; Koch Gabriel S; Planchon Fabrice

来源：Mathematische Annalen, 2013, 355(4): 1527-1559.

DOI：10.1007/s00208-012-0830-0

In this paper we continue to develop an alternative viewpoint on recent studies of Navier-Stokes regularity in critical spaces, a program which was started in the recent work by Kenig and Koch (Ann Inst H Poincar, Anal Non Lin,aire 28(2):159-187, 2011). Specifically, we prove that strong solutions which remain bounded in the space do not become singular in finite time, a known result established by Escauriaza et al. (Uspekhi Mat Nauk 58(2(350)):3-44, 2003) in the context of suitable weak solutions. Here, we use the method of %26quot;critical elements%26quot; which was recently developed by Kenig and Merle to treat critical dispersive equations. Our main tool is a %26quot;profile decomposition%26quot; for the Navier-Stokes equations in critical Besov spaces which we develop here. As a byproduct of this tool, assuming a singularity-producing initial datum for Navier-Stokes exists in a critical Lebesgue or Besov space, we show there is one with minimal norm, generalizing a result of Rusin and Sverak (J Funct Anal 260(3):879-891, 2011).

• 出版日期2013-4