On stationary Navier-Stokes flows around a rotating obstacle in two-dimensions

TL;DR

This paper investigates the existence and behavior of steady two-dimensional fluid flows around a rotating obstacle, establishing conditions for unique solutions and their asymptotic properties at large distances.

Contribution

It provides new results on the existence, uniqueness, and asymptotic behavior of stationary Navier-Stokes flows around rotating obstacles in 2D.

Findings

Unique solutions exist under small rotation speed and force.

Solutions exhibit specific asymptotic decay at infinity.

The analysis advances understanding of rotating obstacle flows in 2D.

Abstract

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.