Leading terms of velocity and its gradient of the stationary rotational viscous incompressible flows with nonzero velocity at infinity

TL;DR

This paper derives asymptotic expansions and decay estimates for velocity and its gradient in stationary rotational viscous incompressible flows around a moving and rotating body, using a fundamental solution approach.

Contribution

It introduces a new method based on a fundamental solution to obtain asymptotic behavior of solutions, differing from previous approaches.

Findings

Asymptotic expansion of velocity and its gradient

Pointwise decay estimates of remainder terms

Application of Guenther and Thomann's fundamental solution

Abstract

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a previous paper, we prove a representation formula for weak solutions of the system. Here the representation formula is used to get an asymptotic expansion of respectively velocity and its gradient, and to establish pointwise decay estimates of remainder terms. Our results are based on a fundamental solution proposed by Guenther and Thomann J. Math. Fluid Mech., 8 (2006), 77-98. We thus present a different approach to this result, besides the one, given by Kyed J. Math. Soc. Japan, 66 (2014), 1-16.