Related papers: Compact support of spherically symmetric equilibri…
The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov-Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of…
We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
Certain steady states of the Vlasov-Poisson system can be characterized as minimizers of an energy-Casimir functional, and this fact implies a nonlinear stability property of such steady states. In previous investigations by Y. Guo and the…
We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry.…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical…
It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the…
We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states…
As is well known from the work of R. Glassey} and J. Schaeffer, the main energy estimates which are used in global existence results for the gravitational Vlasov-Poisson system do not apply to the relativistic version of this system, and…
We prove the existence of static, spherically symmetric solutions of the stellar dynamic Vlasov-Poisson and Vlasov-Einstein systems, which have the property that their spatial support is a finite, spherically symmetric shell with a vacuum…
?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic…
The Nordstr\"om-Vlasov system is a relativistic Lorentz invariant generalization of the Vlasov-Poisson system in the gravitational case. The asymptotic behavior of solutions and the non-linear stability of steady states are investigated. It…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady…
This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson…
The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally…
We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution…
The stability of static solutions of the spherically symmetric, asymptotically flat Einstein-Vlasov system is studied using a Hamiltonian approach based on energy-Casimir functionals. The main result is a coercivity estimate for the…