• Corpus ID: 235435975

2D point vortex dynamics in bounded domains: global existence for almost every initial data

@inproceedings{Donati20212DPV,
  title={2D point vortex dynamics in bounded domains: global existence for almost every initial data},
  author={Martin Donati},
  year={2021}
}
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, meaning that there is no collision between two pointvortices or with the boundary. This extends the work previously done in [13] for the unit disk. The proof requires the construction of a regularized dynamics that approximates the real dynamics and some strong inequalities for the Green’s function of… 

Figures from this paper

H\"older regularity for collapses of point vortices
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

References

SHOWING 1-10 OF 21 REFERENCES
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
Two Dimensional Incompressible Ideal Flow Around a Small Obstacle
Abstract In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle
Self-similar point vortices and confinement of vorticity
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
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
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
Convergence of the point vortex method for the 2-D euler equations
TLDR
This work proves consistency, stability and convergence of the point vortex approximation to the 2-D incompressible Euler equations with smooth solutions to be stable in l p norm for all time.
Mathematical Theory of Incompressible Nonviscous Fluids
This book deals with fluid dynamics of incompressible non-viscous fluids. The main goal is to present an argument of large interest for physics, and applications in a rigorous logical and
Vortex Methods in Two-Dimensional Fluid Dynamics
Euler equations.- Vortex model.- An existence theorem for Euler equations.- Further considerations on vortex model.- A mean field limit.- Navier-Stokes equations.- Diffusion process and Navier-Stokes
Boundary Behaviour of Conformal Maps
1. Some Basic Facts.- 2. Continuity and Prime Ends.- 3. Smoothness and Corners.- 4. Distortion.- 5. Quasidisks.- 6. Linear Measure.- 7. Smirnov and Lavrentiev Domains.- 8. Integral Means.- 9. Curve
Large time behavior in perfect incompressible flows
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and
...
...