• Corpus ID: 244714154

H\"older regularity for collapses of point vortices

@inproceedings{Donati2021HolderRF,
  title={H\"older regularity for collapses of point vortices},
  author={Martin Donati and Ludovic Godard-Cadillac},
  year={2021}
}
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. This consists in a Biot-Savart law with a kernel being a power function of exponent −α. It is proved that, under a standard non-degeneracy hypothesis, the trajectories of the vorticies have a regularity Hölder at T the time of collapse. The Hölder exponent obtained is 1/(α+ 1) and this exponent is proved to be… 

References

SHOWING 1-10 OF 31 REFERENCES
Collapse of generalized Euler and surface quasigeostrophic point vortices.
TLDR
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.
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,
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
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
Quantization and Motion Law for Ginzburg–Landau Vortices
We study the vortex trajectories for the two-dimensional complex parabolic Ginzburg–Landau equation without a well-preparedness assumption. We prove that the trajectory set is rectifiable, and
Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation
We provide a variational construction of special solutions to the generalized surface quasi-geostrophic equations. These solutions take the form of N vortex patches with N-fold symmetry , which are
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
Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid
The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the
Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations
TLDR
A rigorous justification of the point vortex approximation to the family of modified surface quasi-geostrophic (mSQG) equations globally in time in both the inviscid and vanishing dissipative cases is given.
...
1
2
3
4
...