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

Author

Shangkun Weng and Wenqi Lyu

Subjects
Applied Mathematics, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Rotational symmetry, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Dirichlet integral, symbols.namesake, symbols, A priori and a posteriori, Order (group theory), 0101 mathematics, Navier–Stokes equations, Scaling, Weighted energy, Analysis, Mathematics
Abstract

In this paper, we are interested in the decay properties of the axisymmetric solutions to the stationary Navier-Stokes equations in R 3 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.

Published
2020
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