相关论文: Gravitational Collapse for Polytropic Gaseous Star…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
The classical model of an isolated selfrgavitating gaseous star is given by the Euler-Poisson system with a polytropic pressure law $P(\rho)=\rho^\gamma$, $\gamma>1$. For any $1<\gamma<\frac43$, we construct an infinite-dimensional family…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
By the extension of the 3-dimensional analytical solutions of Goldreich and Weber "P. Goldreich and S. Weber, Homologously Collapsing Stellar Cores, Astrophys, J. 238, 991 (1980)" with adiabatic exponent gamma=4/3, to the (classical)…
We find exact and explicit solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously, of a collapsing…
Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397…
Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $\gamma$. We complete the existing literature on the subject by…
We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity when the adiabatic exponent $\gamma$ belongs to…
Using numerical integration, in 1969 Penston [22] and Larson [17] independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $p=k\varrho$,…
This investigation is devoted to the solutions of Einstein's field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial…
We study the threshold of gravitational collapse in spherically symmetric spacetimes governed by the Einstein-Maxwell-Vlasov equations. We numerically construct solutions describing a collapsing distribution of charged matter that either…
Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal ($\gamma=1$) Euler-Poisson equations in $R^{2}$…
We prove nonlinear stability of compactly supported expanding star-solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expanding rate of such…
A self-gravitating homogeneous ball of a fluid with pressure zero where the fluid particles are initially at rest collapses to a point in finite time. We prove that this gravitational collapse can be approximated arbitrarily closely by…
We rigorously construct a family of smooth self-similar solutions to the isentropic gravitational Euler-Poisson system with a polytropic equation of state for polytropic indices lying in the full energy-supercritical range,…
The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed…
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…
We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases…
This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The…
We investigate the structure of self-gravitating polytropic stellar systems. We present a method which allows to obtain approximate analytical solutions, $\psi_{n+\epsilon}({\bf x})$, of the nonlinear Poisson equation with the polytropic…