A logarithmically improved regularity criterion for the Navier–Stokes equations

摘要

In this note we prove a logarithmically improved regularity criterion in terms of the Besov space norm for the Navier–Stokes equations. The result shows that if a mild solution u satisfies ${int_{0}^{T}frac{|u (t,cdot)|_{{dot{B}}_{infty,infty}^{-r}}^{frac{2}{1-r}}}{1+ln(e+| u(t,cdot)|_{H^{s}})}text{d}t infty}$ for some 0 ≤ r 1 and ${sgeqfrac{n}{2}-1}$ , then u is regular at t = T.