On the regularity criterion of axisymmetric weak solutions to the 3D Navier–Stokes equations Original Research Article

In this paper, we consider the regularity criterion of axisymmetric weak solutions to the Navier–Stokes equations in R3R3. Let uu be an axisymmetric weak solution in R3×(0,T)R3×(0,T), View the MathML sourcew=curlu, and wθwθ be the azimuthal component of ww in the cylindrical coordinates. It is proved that uu becomes a regular solution if View the MathML sourcewθ∈L22−s(0,T;M.2,3s), where View the MathML sourceM.2,3s is the critical Morrey–Campanato space.