The Double-Logarithmic Regularity Criterion of Pressure for the 3D Navier–Stokes Equations in the Besov Space - Min Liu; Juan Song; Tian-Li Li (Journal of Mathematics)
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.