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 three-dimensional Navier-Stokes equations, two sufficient conditions such that the horizontal velocity \tilde{u} satisfies \tilde{u}∈L^2(0,T;BMO(R^3)) or \tilde{u}∈ L^{2/1+r}(0,T; \dot{B}^r_{∞,∞}(R^3)) for 0 < r < 1 are considered.