Related papers: Theorems on existence and global dynamics for the …
A global existence theorem, with respect to a geometrically defined time, is shown for Gowdy symmetric globally hyperbolic solutions of the Einstein-Vlasov system for arbitrary (in size) initial data. The spacetimes being studied contain…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In…
This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the…
This paper explores the status of some notions which are usually associated to time, like datations, chronology, durations, causality, cosmic time and time functions in the Einsteinian relativistic theories. It shows how, even if some of…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
In this paper, we elucidate the problem of gravitating Skyrmion governed by field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry has to be assumed and both the metric functions…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…
The fundamental physical object of the Global Time Theory is a three-dimensional curved space dynamically developing in global time. The equations of its dynamics are derived from the Lagrangian, and the Hamiltonian of ravitation turns out…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due…
The paper presents a generalization and further development of our recent publications where solutions of the Klein-Fock-Gordon equation defined on a few particular $D=(2+1)$-dim static space-time manifolds were considered. The latter…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
We analyze the relativistic Euler equations of conservation laws of baryon number and momentum with a general pressure law. The existence of global-in-time bounded entropy solutions for the system is established by developing a compensated…
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…