2011/09/06 by Christophe Lacave, Lacave, Christophe · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1109.1153
openalex publication_date 2011/09/06 · arxiv created 2013/10/19 · arxiv updated 2013/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The existence of a solution to the two dimensional incompressible Euler equations in singular domains was established in [Gérard-Varet and Lacave, The 2D Euler equation on singular domains, submitted]. The present work is about the uniqueness of such a solution when the domain is the exterior or the interior of a simply connected set with corners, although the velocity blows up near these corners. In the exterior of a curve with two end-points, it is showed in [Lacave, Two Dimensional Incompressible Ideal Flow Around a Thin Obstacle Tending to a Curve, Ann. IHP, Anl 26 (2009), 1121-1148] that this solution has some interesting properties, as to be seen as a special vortex sheet. Therefore, we prove the uniqueness, whereas the problem of general vortex sheets is open.