# Confinement of vorticity in two dimensional ideal incompressible exterior flow

@article{Iftimie2006ConfinementOV,
title={Confinement of vorticity in two dimensional ideal incompressible exterior flow},
author={Dragos Iftimie and Milton C. Lopes Filho and Helena J. Nussenzveig Lopes},
journal={Quarterly of Applied Mathematics},
year={2006},
volume={65},
pages={499-521}
}
• Published 22 August 2006
• Mathematics
• Quarterly of Applied Mathematics
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 like O(t (1/2)+" ), for any " > 0. In addition, if the domain is the exterior of a disk, then the…
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## References

SHOWING 1-10 OF 25 REFERENCES

### Two-dimensional incompressible viscous flow around a small obstacle

• Mathematics
• 2003
In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω0 and the circulation γ of the initial flow

### Two Dimensional Incompressible Ideal Flow Around a Small Obstacle

• Mathematics
• 2003
Abstract In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle

### Large smoke rings with concentrated vorticity

In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present,

### On the motion of a vortex ring with a sharply concentrated vorticity

• Mathematics, Environmental Science
• 2000
We study an incompressible non-viscous fluid with axial symmetry without swirl, in the case when the vorticity is supported in an annulus. It is well known that there exist particular initial data

### On the Growth of the Vorticity Support for an Incompressible Non-viscous Fluid in a Two-dimensional Exterior Domain

We study the time evolution of the support of a positive vorticity for a non-viscous incompressible fluid evolving in R 2 - D, where D is a compact domain with smooth boundary. We bound its growth.

### On the Inviscid Limit for a Fluid with a Concentrated Vorticity

Abstract:We study the time evolution of a viscous incompressible fluid in ℝ2 when the initial vorticity is sharply concentrated in N regions of diameter ε. We prove that in the zero viscosity limit

### Vortices and localization in Euler flows

• Mathematics
• 1993
We study the time evolution of a non-viscous incompressible two-dimensional fluid when the initial vorticity is concentrated inN small disjoint regions of diameter ε. We prove that the time evolved

### Large Time Behavior for Vortex Evolution in the Half-Plane

• Mathematics
• 2003
Abstract: In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states

### Bounds on the growth of the support of a vortex patch

We study the time evolution of the support of a vortex patch evolving in ℝ2 according to the Euler Equation for an incompressible fluid and we bound its growth. Furthermore we discuss the same