Remarks on the Regularity Criteria of Three-dimensional Navier-Stokes Equations in Margin Case

Abstract

In the study of the regularity criteria for Leray weak solutions to threedimensional Navier-Stokes equations, two sufficient conditions such that the horizontal velocity ũ satisfies ũ∈ L2(0,T;BMO(R)) or ũ∈ L2/1+r(0,T; Ḃr ∞,∞(R )) for 0< r< 1 are considered. AMS Subject Classifications: 35Q35 Chinese Library Classifications: O175.24