Anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces with applications to the axisymmetric Navier-Stokes equations

In this paper, we establish several new anisotropic Hardy-Sobolev inequalities in mixed Lebesgue spaces and mixed Lorentz spaces, which covers many known corresponding results. As an application, this type of inequalities allows us to generalize some regularity criteria of the 3D axisymmetric Navier-Stokes equations.Comment: 18 page