相关论文: Future Stability of Tilted Two-Fluid Bianchi I Spa…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The…
We show that any 3+1-dimensional Milne model is future nonlinearly, asymptotically stable in the set of solutions to the Einstein-Vlasov system. For the analysis of the Einstein equations we use the constant-mean-curvature-spatial-harmonic…
We investigate the integrability of cosmic strings in Bianchi III space-time in presence of a bulk viscous fluid by applying a new technique. The behaviour of the model is reduced to the solution of a single second order nonlinear…
In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…
We present a dynamical analysis in terms of new expansion-normalized variables for homogeneous and anisotropic Bianchi-I spacetimes in $f(R)$ gravity in the presence of anisotropic matter. With a suitable choice of the evolution parameter,…
We consider solutions to the full (non-isentropic) two-dimensional Euler equations that are constant in time and along rays emanating from the origin. We prove that for a polytropic equation of state, entropy admissible solutions in…
We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium…
We study the problem of evolution of bulk 5-fluids having an embedded braneworld with a flat, de Sitter, or anti-de Sitter geometry. We introduce new variables to express the Einstein equations as a dynamical system that depends on the…
Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and…
Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…
We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive…
We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…
In the present paper we discuss dynamic of anisotropic Bianchi I Universe filled by the perfect fluid in teleparallel $f(T)$-gravity. By using as analytical as numerical approaches we confirm the main results of previous authors such as…
We establish the future nonlinear stability of a large class of FLRW models as solutions to the Einstein-Dust system. We consider the case of a vanishing cosmological constant, which in particular implies that the expansion rate of the…
We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq 1/3$,…
We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assume a realistic barotropic equation of state. Equilibria of…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
We consider solutions of the 2-d compressible Euler equations that are steady and self-similar. They arise naturally at interaction points in genuinely multi-dimensional flow. We characterize the possible solutions in the class of flows…