Silvia Caprino

ON THE TWO-DIMENSIONAL VLASOV-HELMHOLTZ EQUATION WITH INFINITE MASS

ABSTRACT We prove existence and uniqueness of the solutions to the Vlasov-Helmholtz equation in two dimensions in the case of unbounded mass.

Time evolution of infinitely many particles: An existence theorem

In this paper we deal with systems of infinitely many particles in ℝ3, given by a two-body, short-range potential and an external potential, depending on the position of the particles. We show the existence of dynamics for a set of initial configurations, which has measure one with respect to the Gibbs measure induced by a suitable family of Hamiltonians.

Time Evolution of a Vlasov-Poisson Plasma with Infinite Charge in ℝ3

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a one-species plasma evolving in ℝ3, whose particles interact via the Coulomb potential. It is assumed that initially the particles have bounded velocities and are distributed according to a non integrable density.

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.

On nonlinear stablility of stationary of planar Euler flows in an unbounded strip

THE LIAPUNOV stability for some stationary states of the two-dimensional Euler equation has been investigated by Arnold [ 11. He constructed a Liapunov functional by means of the energy, the vorticity and other eventually conserved quantities of the system, and established sufficient conditions for the stability of the steady flows under consideration. (For a review on the Arnold method and its applications see [2].) This method works only when dealin g with smooth quantities. Moreover, the domain containing the fluid has to be bounded. On the other hand, there are many physical problems of some interest in which one or both these conditions are missing. Some recent results concerning stability in the non smooth case have been obtained in [3,4]. In particular, in [4] the authors suppose that the fluid flows in a periodic channel. This kind of spatial symmetry allows us to introduce a first integral, to be used as a Liapunov functional, and to prove a stability result for nonsmooth stationary states. In this paper, we go further in this direction and prove an analogous result for a fluid in an unbounded strip. In analogy with [4], we introduce a conserved functional and show that the stationary (possibly nonsmooth) states under consideration are an absolute minimum (or maximum) for this functional. This enables us to state a stability result in terms of two different “stability measures”. More precisely, we show that if the initial perturbation of the vorticity is small in the L,-norm, then the corresponding velocity field. at any point in the strip, stays near the unperturbed one, uniformly in time. In Section 2 we give some preliminary notations and state our main result, which is proved in Section 3. We postpone until the Appendix the proof of the existence and uniqueness of the weak solutions of the Euler equation in a strip and stress some properties that are useful in our context.

On the Magnetic Shield for a Vlasov–Poisson Plasma

We study the screening of a bounded body

On the plasma-charge model

\Gamma

On a charge interacting with a plasma of unbounded mass

Γ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of