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We develop a Birman-Schwinger principle for the spherically symmetric, asymptotically flat Einstein-Vlasov system. It characterizes stability properties of steady states such as the positive definiteness of an Antonov-type operator or the…

Analysis of PDEs · Mathematics 2025-08-27 Sebastian Günther , Gerhard Rein , Christopher Straub

In this paper, the global existence of smooth solution and the long-time asymptotic stability of the equilibrium to vacuum free boundary problem of the spherically symmetric Euler equations with damping and solid core have been obtained for…

Analysis of PDEs · Mathematics 2024-02-22 Yan-Lin Wang

We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equation of states which cover polytropic gaseous stars indexed…

Analysis of PDEs · Mathematics 2019-01-25 Juhi Jang , Tetu Makino

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Paul Lasky , Anthony Lun

This paper proves the nonlinear asymptotic stability of the Lane-Emden solutions for spherically symmetric motions of viscous gaseous stars if the adiabatic constant $\gamma$ lies in the stability range $(4/3, 2)$. It is shown that for…

Analysis of PDEs · Mathematics 2015-12-29 Tao Luo , Zhouping Xin , Huihui Zeng

The Einstein-Vlasov-Maxwell (EVM) system can be viewed as a relativistic generalization of the Vlasov-Poisson (VP) system. As it is proved below, one of nice property obeys by the first system is that the strong energy condition holds and…

General Relativity and Quantum Cosmology · Physics 2007-05-23 P. Noundjeu

The particle density distribution emerging from the solution of the Vlasov equation for relativistic, non-interacting particles with spherically symmetric initial conditions is shown to exhibit a shell-like structure for late fixed times in…

Nuclear Theory · Physics 2008-11-26 Carsten Greiner , Dirk-Hermann Rischke

We study the linear stability of vacuum static, spherically symmetric solutions to the gravitational field equations of the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories (STT) of gravity, restricting ourselves to nonphantom…

General Relativity and Quantum Cosmology · Physics 2023-11-14 Kirill A. Bronnikov , Sergei V. Bolokhov , Milena V. Skvortsova , Kodir Badalov , Rustam Ibadov

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…

Mathematical Physics · Physics 2015-05-14 Simone Calogero , Juan Calvo , Óscar Sánchez , Juan Soler

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is…

General Relativity and Quantum Cosmology · Physics 2017-03-03 K. A. Bronnikov , J. C. Fabris , O. F. Piattella , E. C. Santos

We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…

General Relativity and Quantum Cosmology · Physics 2009-11-11 J. Mark Heinzle , Claes Uggla

The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the…

Analysis of PDEs · Mathematics 2016-10-12 Tao Luo , Zhouping Xin , Huihui Zeng

In this paper, we consider the global spherically symmetric strong solutions to the compressible Navier-Stokes equations with far-field vacuum and density-dependent degenerate viscosity, following the framework proposed by Bresch-Vasseur-Yu…

Analysis of PDEs · Mathematics 2026-05-05 Xingyang Zhang

We re-examine the dynamical stability of the nakedly singular, static, spherical ly symmetric solutions of the Einstein-Klein Gordon system. We correct an earlier proof of the instability of these solutions, and demonstrate that there are…

General Relativity and Quantum Cosmology · Physics 2010-11-19 M. A. Clayton , L. Demopoulos , J. Legare

In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle accelerator. We show existence and uniqueness of global…

Analysis of PDEs · Mathematics 2024-06-05 Ludovic Cesbron , Maxime Herda

The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…

General Relativity and Quantum Cosmology · Physics 2015-06-25 J. Kijowski , G. Magli , D. Malafarina

Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…

General Relativity and Quantum Cosmology · Physics 2025-12-09 David Bick

We prove that for large enough data, the life span of smooth solutions to the Cauchy problem for the following two quasilinear hyperbolic systems is finite: (1) equations of relativistic compressible fluid dynamics, (2) equations of plasma…

Analysis of PDEs · Mathematics 2007-05-23 Yan Guo , A. Shadi Tahvildar-Zadeh

We study the properties of a system consisting of an uncharged spherically symmetric two dimensional extended object which encloses a stationary point charge placed in the shell's center. We show that there can be a static and stable…

General Relativity and Quantum Cosmology · Physics 2009-02-09 Eduardo I. Guendelman , Idan Shilon

The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic…

Analysis of PDEs · Mathematics 2024-03-13 Mingjie Li , Masahiro Suzuki