• Corpus ID: 247447123

On the dynamics of vortices in viscous 2D flows

  title={On the dynamics of vortices in viscous 2D flows},
  author={Stefano Ceci and Christian Seis},
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 near a system of interacting point vortices introduced by Helmholtz and Kirchhoff. Our work extends the previous results in the literature in three ways: The initial vorticity is concentrated in a weak (Wasserstein) sense, it is merely Lp integrable for some p > 2, and the estimates we derive are… 


Vortices and localization in Euler flows
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 motion of a vortex ring with a sharply concentrated vorticity
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 vanishing viscosity limit for two-dimensional Navier–Stokes equations with singlular initial data
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 Cauchy Problem for Axi-Symmetric Vortex Rings
We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data
On the Vortex Filament Conjecture for Euler Flows
In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in $${\mathbb{R}^{3}}$$R3, we
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
Gluing Methods for Vortex Dynamics in Euler Flows
A classical problem for the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain is that of finding regular solutions with highly concentrated vorticities around N
Interaction of Vortices in Weakly Viscous Planar Flows
We consider the inviscid limit for the two-dimensional incompressible Navier–Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that
Stability and Interaction of Vortices in Two-Dimensional Viscous Flows
The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the
The inviscid limit for non-smooth vorticity
We consider the inviscid limit of the incompressible Navier-Stokes equations for the case of two-dimensional non-smooth initial vorticities in Besov spaces. We obtain uniform rates of L convergence