Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

TL;DR

This paper analyzes the asymptotic behavior of viscous incompressible flow around a rotating body, showing that the flow can be decomposed into a dominant fundamental solution component plus a rapidly decaying remainder, advancing understanding of such flows.

Contribution

It provides a refined asymptotic decomposition of solutions to the Navier-Stokes system with rotational effects, improving previous theoretical results.

Findings

Velocity decomposes into a fundamental solution term plus a faster decaying remainder.

The decay rate of the remainder exceeds that of the Oseen tensor.

Enhances the understanding of flow behavior around rotating bodies at infinity.

Abstract

We consider weak (''Leray'') solutions to the stationary Navier-Stokes system with Oseen and rotational terms, in an exterior domain. It is shown the velocity may be split into a constant times the first column of the fundamental solution of the Oseen system, plus a remainder term decaying pointwise near infinity at a rate which is higher than the decay rate of the Oseen tensor. This result improves the theory by M. Kyed, Asymptotic profile of a linearized flow past a rotating body, Q. Appl. Math. 71 (2013), 489-500.