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

TL;DR

This paper investigates how solutions to 2D incompressible Euler equations behave asymptotically as a smooth obstacle shrinks to a curve, extending previous results from point to curve limits.

Contribution

It generalizes prior work by analyzing the flow around a thin obstacle tending to a curve, providing new insights into the asymptotic behavior of solutions.

Findings

Extended asymptotic analysis from point to curve obstacle limits.

Established convergence results for flow solutions as obstacle becomes thin.

Connected the behavior of flow around shrinking obstacles to idealized curve limits.

Abstract

In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by Iftimie, Lopes Filho and Nussenzveig Lopes, obtained in the context of an obstacle tending to a point, see [Comm. PDE, {\bf 28} (2003), 349-379].