# Euler evolution for singular initial data and vortex theory: A global solution

@article{Marchioro1988EulerEF, title={Euler evolution for singular initial data and vortex theory: A global solution}, author={Carlo Marchioro}, journal={Communications in Mathematical Physics}, year={1988}, volume={116}, pages={45-55} }

We study the evolution of a two-dimensional, incompressible, ideal fluid in a case in which the vorticity is concentrated in small disjoint regions and we prove, globally in time, its connection with the vortex model.

## 30 Citations

Point Vortices and Localization in Euler Flows

- Mathematics
- 1993

We study the time evolution of an inviscid incompressible two-dimensional fluid when the initial vorticity is sharply concentrated in N small regions of diameter e. We give a rigourous proof of the…

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…

On the Inviscid Limit for a Fluid with a Concentrated Vorticity

- Mathematics
- 1998

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…

Bounds on the growth of the support of a vortex patch

- Mathematics
- 1994

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…

Long Time Evolution of Concentrated Euler Flows with Planar Symmetry

- PhysicsSIAM J. Math. Anal.
- 2018

A toy model is analyzed that shows a similar behavior to an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks, showing that in some cases this happens for quite long times.

On the vanishing viscosity limit for two-dimensional Navier–Stokes equations with singlular initial data

- Mathematics
- 1990

We study the solutions of the Navier–Stokes equations when the initial vorticity is concentrated in small disjoint regions of diameter ϵ. We prove that they converge, uniformily in ϵ. for vanishing…

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…

Euler evolution of a concentrated vortex in planar bounded domains

- Mathematics, Physics
- 2018

In this paper, we consider the time evolution of an ideal fluid in a planar bounded domain. We prove that if the initial vorticity is supported in a sufficiently small region with diameter…

Concentrated Euler flows and point vortex model

- Mathematics
- 2015

This paper is an improvement of previous results on concentrated Euler flows and their connection with the point vortex model. Precisely, we study the time evolution of an incompressible two…

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