Green tensor of the Stokes system and asymptotics of stationary Navier-Stokes flows in the half space

TL;DR

This paper derives refined estimates for the Green tensor of the stationary Stokes system in the half space and analyzes the asymptotic behavior of stationary Navier-Stokes flows, including special cases like axisymmetric solutions.

Contribution

It provides new refined estimates of the Green tensor and detailed asymptotic analysis of stationary flows in half space and exterior domains, including self-similar solutions.

Findings

Refined estimates of the Green tensor for the Stokes system.

Asymptotic descriptions of stationary Navier-Stokes flows in half space.

Analysis of axisymmetric self-similar solutions.

Abstract

We derive refined estimates of the Green tensor of the stationary Stokes system in the half space. We then investigate the spatial asymptotics of stationary solutions of the incompressible Navier-Stokes equations in the half space. We also discuss the asymptotics of fast decaying flows in the whole space and exterior domains. In the Appendix we consider axisymmetric self-similar solutions.