Evelyne Miot

The Cauchy Problem for the 3-D Vlasov–Poisson System with Point Charges

In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov–Poisson system in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result (Caprino and Marchioro in Kinet. Relat. Models 3(2):241–254, 2010).

UNIQUENESS FOR THE VORTEX-WAVE SYSTEM WHEN THE VORTICITY IS CONSTANT NEAR THE POINT VORTEX

We prove uniqueness for the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti in the case where the vorticity is initially constant near the point vortex. Our method relies on the Eulerian approach for this problem and in particular on the formulation in terms of the velocity.

On the Attractive Plasma-Charge System in 2-d

We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a global in time solution, assuming a suitable initial distribution of the velocities of the plasma particles. Uniqueness remains unsolved.

Global existence and collisions for symmetric configurations of nearly parallel vortex filaments

Abstract We consider the Schrodinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran (1995) [17] to modelize the dynamics of N nearly parallel vortex filaments in a 3-dimensional homogeneous incompressible fluid. The known large time existence results are due to C. Kenig, G. Ponce and L. Vega (2003) [16] and concern the interaction of two filaments and particular configurations of three filaments. In this article we prove large time existence results for particular configurations of four nearly parallel filaments and for a class of configurations of N nearly parallel filaments for any N ⩾ 2 . We also show the existence of travelling wave type dynamics. Finally we describe configurations leading to collision.

On the Kac model for the Landau equation

We introduce a

Collisions of vortex filament pairs

N

Existence of a Weak Solution in L (p) to the Vortex-Wave System

-particle system which approximates, in the mean-field limit, the solutions of the Landau equation with Coulomb singularity. This model plays the same role as the Kacs model for the homogeneous Boltzmann equation. We use compactness arguments following [11].

DYNAMICS OF VORTICES FOR THE COMPLEX GINZBURG-LANDAU EQUATION

We consider the problem of collisions of vortex filaments for a model introduced by Klein et al. (J Fluid Mech 288:201–248, 1995) and Zakharov (Sov Phys Usp 31(7):672–674, 1988, Lect. Notes Phys 536:369–385, 1999) to describe the interaction of almost parallel vortex filaments in three-dimensional fluids. Since the results of Crow (AIAA J 8:2172–2179, 1970) examples of collisions are searched as perturbations of antiparallel translating pairs of filaments, with initial perturbations related to the unstable mode of the linearized problem; most results are numerical calculations. In this article, we first consider a related model for the evolution of pairs of filaments, and we display another type of initial perturbation leading to collision in finite time. Moreover, we give numerical evidence that it also leads to collision through the initial model. We finally study the self-similar solutions of the model.

Uniqueness for the 2-D Euler equations on domains with corners

The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this article, we prove existence of a weak solution to this system with an initial background vorticity in Lp, p>2, up to the time of first collision of point vortices.