on the regularity criterion of axisymmetric weak solutions to the 3d navier–stokes equations

in this paper, we consider the regularity criterion of axisymmetric weak solutions to the navier–stokes equations in r³. let u be an axisymmetric weak solution in r³ × (0, t ), w = curl u, and w^θ be the azimuthal component of w in the cylindrical coordinates.