The Double-Logarithmic Regularity Criterion of Pressure for the 3D Navier–Stokes Equations in the Besov Space

Abstract

In the paper, we consider the regularity of the weak solutions for the incompressible 3D Navier–Stokes (N–S) equations. Our main result is the double-logarithmic regularity criterion of pressure for the 3D Navier–Stokes equations in the Besov space. ∫0TπB˙∞,∞−3/qp/e+lne+πB˙∞,∞−3/qlne+lne+πB˙∞,∞−3/qdt<∞, 2/q+3/q=2,3≤q≤∞. Our results extend and generalize previous works.