Two Dimensional Incompressible Viscous Flow Around a Thin Obstacle Tending to a Curve

TL;DR

This paper investigates the behavior of two-dimensional incompressible viscous flow around a thin obstacle shrinking to a curve, demonstrating convergence to Navier-Stokes solutions and establishing uniqueness of the limit.

Contribution

It extends previous work on Euler equations to viscous flows, proving convergence and uniqueness for Navier-Stokes solutions around shrinking obstacles.

Findings

Convergence of viscous flow to Navier-Stokes solution

Uniqueness of the limit solution

Extension of prior Euler results to viscous case

Abstract

In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem in the viscous case, proving convergence to a solution of the Navier-Stokes equations in the exterior of a curve. The uniqueness of the limit solution is also shown.