Uniqueness for Two-Dimensional Incompressible Ideal Flow on Singular Domains

Uniqueness for Two-Dimensional Incompressible Ideal Flow on Singular Domains

We prove uniqueness of the weak solution of the Euler equations for compactly supported, single signed and bounded initial vorticity in simply connected planar domains with corners forming angles larger than π/2. In this type of domain, the velocity is not log-lipschitz and does not belong to W 1,p for all p, which is the standard regularity for the Yudovich’s arguments. Thanks to the explicit ...

Two Dimensional Incompressible Ideal Flow Around a Small Curve

Two dimensional incompressible ideal flow around a small obstacle

In this article we study the asymptotic behavior of incompressible, ideal, timedependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the equation satisfied by the limit flow. We will see that the asymptotic behavior depends on γ, the circulation around the obstacle. For smooth flow around a si...

On the evolution of a singular vortex patch in a two-dimensional incompressible fluid flow

The angle evolution of a tangent-slope discontinuity on a singular vortex patch, i.e. a patch of vorticity with tangent discontinuities in its boundary, is studied from a numerical and theoretical point of view. Different numerical examples show that the angle shrinks for an initial angle less than 90◦, the angle widens when the initial angle is greater than 90◦ or is approximately preserved fo...

Two-dimensional Incompressible Ideal Flows in a Noncylindrical Material Domain

Abstract. The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a prescribed motion. We prove existence of a weak solution for initial vorticity in L, for p > 1. This work complements a similar result by C. He and L. Hsiao...