An anisotropic Sobolev–Hardy inequality with application to 3D axisymmetric Navier–Stokes equations. Issue 2 (25th January 2020) - Yu, Huan
ABSTRACT: In this paper, we first establish a new anisotropic Sobolev–Hardy inequality in which anisotropic singular weights are permitted. As an application, we study the three-dimensional axisymmetric Navier–Stokes system with non-zero swirl and obtain the global well-posedness result if the angular velocity u θ satisfies sup 0 < t < T ∥ z u θ ( ⋅, t ) ∥ L ∞ ( r ≤ r 0 ) ≤ ϵ, r 0 ∈ ( 0, 1 2 ) .