Two Dimensional Incompressible Ideal Flow Around a Small Curve
Analysis of PDEs
2011-02-07 v1
Abstract
We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig Lopes, Two Dimensional Incompressible Ideal Flow Around a Small Obstacle, Comm. PDE, 28 (2003), 349-379] and [Lacave, Two Dimensional Incompressible Ideal Flow Around a Thin Obstacle Tending to a Curve, Ann. IHP, Anl, 26 (2009), 1121-1148]. The second goal of this work is to complete the previous article, in defining the way the obstacles shrink to a curve. In particular, we give geometric properties for domain convergences in order that the limit flow be a solution of Euler equations.
Cite
@article{arxiv.1102.0843,
title = {Two Dimensional Incompressible Ideal Flow Around a Small Curve},
author = {Christophe Lacave},
journal= {arXiv preprint arXiv:1102.0843},
year = {2011}
}