Decay rates of second order derivatives of axisymmetric D-solutions to the stationary Navier-Stokes equations

Abstract

In this paper, we are interested in the decay properties of the axisymmetric solutions to the stationary Navier-Stokes equations in R3 with finite Dirichlet integral. We establish some new a priori decay rates for the second order derivatives of the velocity. The result is obtained by combining the weighted energy estimates, the Brezis-Galleout inequality and the scaling argument.