On Navier-Stokes equations arising from the rotation of an obstacle in a fluid

TL;DR

This paper studies modified Navier-Stokes equations for fluid flow around a rotating obstacle, proving existence and regularity of solutions at large distances using weighted Sobolev spaces.

Contribution

It introduces a framework for analyzing Navier-Stokes equations with rotation effects and establishes existence and regularity results in weighted Sobolev spaces.

Findings

Existence of solutions under certain conditions

Regularity of solutions at infinity

Use of weighted Sobolev spaces for large-distance behavior

Abstract

We consider the modified Navier-Stokes equations in R3 describing the motion of a fluid in the presence of a rotating rigid body. Weighted Sobolev spaces are used to describe the behavior of solutions at large distances. Under suitable assumptions, w e prove the existence and regularity of solutions satisfying appropriate conditions at infinity.