3D viscous incompressible fluid around one thin obstacle

TL;DR

This paper investigates the behavior of 3D viscous incompressible fluids around a shrinking obstacle, showing that a curve obstacle has no impact on the fluid flow, indicating it acts as a removable singularity.

Contribution

It demonstrates that a solid curve obstacle in 3D viscous flow does not influence the fluid, extending understanding of singularities in Navier-Stokes solutions.

Findings

A solid curve obstacle is a removable singularity for Navier-Stokes equations.

The asymptotic behavior of solutions is characterized as the obstacle shrinks.

The obstacle's influence diminishes to zero as it reduces to a curve or surface.

Abstract

In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular, we will prove that a solid curve has no effect on the motion of a viscous fluid, so it is a removable singularity for these equations.