Confinement of vorticity in two dimensional ideal incompressible exterior flow

A ug 2 00 6 Confinement of vorticity in two dimensional ideal incompressible exterior flow

In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro’s paper is that solutions of the incompressible 2D Euler equations with compactly supported nonnegative initial vorticity in the exterior of a connected bounded region have vorticity support with diameter growing at most...

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...

An Initial Value Problem for Two-dimensional Ideal Incompressible Fluids with Continuous Vorticity

We study an initial value problem for the two-dimensional Euler equation. In particular, we consider the case where initial data belongs to a critical or subcritical Besov space, and initial vorticity is continuous with compact support. Under these assumptions, we conclude that the solution to the Euler equation loses an arbitrarily small amount of regularity as time evolves.