1,839 research outputs found
On the gyrokinetic limit for the two-dimensional Vlasov-Poisson system
We investigate the gyrokinetic limit for the Vlasov-Poisson system in two
dimensions, in the regime studied by Golse and Saint-Raymond. We present
another proof of convergence to the Euler equation under several assumptions on
the energy and on the norms of the initial data
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
Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces
In this paper, we establish uniqueness of the solution of the Vlasov-Poisson
system with spatial density belonging to a certain class of Orlicz spaces. This
extends the uniqueness result of Loeper (which holds for uniformly bounded
density) and the uniqueness result of the second author. Uniqueness is a direct
consequence of our main result, which provides a quantitative stability
estimate for the Wasserstein distance between two weak solutions with spatial
density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability
for mean-field PDEs. Our proofs are built on the second-order structure of the
underlying characteristic system associated to the equation
Collisions of vortex filament pairs
We consider the problem of collisions of vortex filaments for a model
introduced by Klein, Majda and Damodaran, and Zakharov to describe the
interaction of almost parallel vortex filaments in three-dimensional fluids.
Since the results of Crow 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
Polynomial propagation of moments and global existence for a Vlasov-Poisson system with a point charge
In this paper, we extend to the case of initial data constituted of a Dirac
mass plus a bounded density (with finite moments) the theory of Lions and
Perthame [6] for the Vlasov-Poisson equation. Our techniques also provide
polynomially growing in time estimates for moments of the bounded density.Comment: 27 pages; new version: few typos have been corrected, the
introduction has been modifie
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