相关论文: Isotropic cosmological singularities 3: The Cauchy…

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy…

We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy…

We prove well-posedness of the initial value problem for the Einstein equations for spatially-homogeneous cosmologies with data at an isotropic cosmological singularity, for which the matter content is either a cosmological constant with…

The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions…

Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at…

We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…

Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.

We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are…

We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…

This paper is devoted to consideration of the theory of collisionless statistical systems with interparticle scalar interaction. The mathematical model of such systems is constructed and the exact solution of Vlasov equation for isotropic…

We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…

The Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and…

In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the…

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy…

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…

We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.

One of the possible applications of macroscopic Einstein equations has been considered. So, the nonsingular isotropic and uniform cosmological model is built. The cosmological consequences of this model are agree with conclusions of…

Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…

The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and…