• Corpus ID: 55337397

# Concentrated Euler flows and point vortex model

```@inproceedings{Caprini2015ConcentratedEF,
title={Concentrated Euler flows and point vortex model},
author={Lorenzo Caprini and Carlo Marchioro},
year={2015}
}```
• Published 2015
• Mathematics
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 dimensional Euler fluid when the initial vorticity is concentrated in N disjoint regions of diameter ✏. We show that the evolved vorticity is concentrated in N regions of diameter d, d  b ✏ (b independent of ✏) for any ↵ < 1/2. The connection is obtained as ✏ ! 0. 1 – Introduction and main result In the…
Vortex dynamics for 2D Euler flows with unbounded vorticity
• Mathematics
• 2019
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the
Location of concentrated vortices in planar steady Euler flows
• Mathematics
• 2021
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity belongs to L, p > 2, and is sharply concentrated in a finite number of regions of small diameter in a
On the dynamics of point vortices for the two-dimensional Euler equation with Lp vorticity
• Mathematics, Physics
Philosophical Transactions of the Royal Society A
• 2022
We study the evolution of solutions to the two-dimensional Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that
On the dynamics of vortices in viscous 2D flows
• Mathematics
• 2022
We study the 2D Navier–Stokes solution starting from an initial vorticity mildly concentrated near N distinct points in the plane. We prove quantitative estimates on the propagation of concentration
Self-similar point vortices and confinement of vorticity
• Physics, Mathematics
• 2018
ABSTRACT This papers deals with the large time behavior of solutions of the incompressible Euler equations in dimension 2. We consider a self-similar configuration of point vortices which grows like
On the dynamics of point vortices for the 2D Euler equation with \$L^p\$ vorticity
• Mathematics, Physics
• 2021
We study the evolution of solutions to the 2D Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the
Time evolution of vortex rings with large radius and very concentrated vorticity
• Physics
• 2021
We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii ≈ r0 and thickness ε. We prove that when r0 =
Ju l 2 02 1 On the dynamics of point vortices for the 2 D Euler equation with L p vorticity
• Mathematics, Physics
• 2021
We study the evolution of solutions to the 2D Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the
Long Time Evolution of Concentrated Euler Flows with Planar Symmetry
• Physics
SIAM 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.