相关论文: Virial inequalities for steady states in relativis…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
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…
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 review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…
The Nordstr\"om-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The study of this model will probably lead to a…
We study a Newtonian model which allows us to describe some extremely flat objects in galactic dynamics. This model is described by a partial differential equation system called Vlasov-Poisson, whose solutions describe the temporal…
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…
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 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…
Families of steady states of the spherically symmetric Einstein-Vlasov system are constructed, which are parametrized by the central redshift. It is shown that as the central redshift tends to zero, the states in such a family are well…
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…
We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general,…
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 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…
The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state…
The Nordstr\"om-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a-priori-bounds on the solutions of this system, which together with energy estimates and the smoothing effect of…
We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…
We prove the existence and stability of flat steady states of the Vlasov-Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by Guo and Rein for this type of problems…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of…