• Corpus ID: 244714154

H\"older regularity for collapses of point vortices

  title={H\"older regularity for collapses of point vortices},
  author={Martin Donati and Ludovic Godard-Cadillac},
The first part of this article studies the collapses of point-vortices for the Euler equation in the plane and for surface quasi-geostrophic equations in the general setting of α models. In these models the kernel of the Biot-Savart law is a power function of exponent − α . It is proved that, under a standard non-degeneracy hypothesis, the trajectories of the point-vortices have a H¨older regularity up to, and including, the time of collapse. The H¨older exponent obtained is 1 / ( α + 1) and… 


Collapse of generalized Euler and surface quasigeostrophic point vortices.
Point-vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the stream function, and it is shown that for SQG the collapse can be either self-similar or non-self-similar.
Vortex collapses for the Euler and Quasi-Geostrophic models
This article studies point-vortex models for the Euler and surface quasi-geostrophic equations. In the case of an inviscid fluid with planar motion, the point-vortex model gives account of dynamics
Finite-time Collapse of Three Point Vortices in the Plane
We investigate the finite-time collapse of three point vortices in the plane utilizing the geometric formulation of three-vortexmotion from Krishnamurthy, Aref and Stremler (2018) Phys. Rev. Fluids
Self-similar motion of three point vortices
One of the counter-intuitive results in the three-vortex problem is that the vortices can converge on and meet at a point in a finite time for certain sets of vortex circulations and for certain
2D point vortex dynamics in bounded domains: global existence for almost every initial data
In this paper, we prove that in bounded planar domains with C2,α boundary, for almost every initial condition in the sense of the Lebesgue measure, the point vortex system has a global solution,
Desingularization of Vortices for the Euler Equation
We study the existence of stationary classical solutions of the incompressible Euler equation in the planes that approximate singular stationary solutions of this equation. The construction is
Burst of Point Vortices and Non-uniqueness of 2D Euler Equations
We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist
Weak vorticity formulation of the incompressible 2D Euler equations in bounded domains
Abstract In this article we examine the interaction of incompressible 2D flows with material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components
Topological regularizations of the triple collision singularity in the 3-vortex problem
The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition for vorticities to have the triple collision, the main results are summarized as
Motion of three vortices
A qualitative analysis of the motion of three point vortices with arbitrary strengths is given. This simplifies and extends recent work by Novikov on the motion of three identical vortices. Using a