Related papers: Global existence of the solution to Einstein-Maxwe…

We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…

We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…

It is well-known that small, regular, spherically symmetric characteristic initial data to the Einstein-scalar-field system which are decaying towards (future null) infinity give rise to solutions which are foward-in-time global (in the…

We establish probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency…

These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…

We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in…

We prove the existence of global solutions to the focusing energy-supercritical semilinear wave equation in R^{3+1} for arbitrary outgoing large initial data, after we modify the equation by projecting the nonlinearity on outgoing states.

The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The…

In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with…

We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach shows that the Einstein-vacuum and the Einstein-scalar field equations with general…

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the…

The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the…

In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…

This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…

We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus…

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is…

In this paper, we consider the 1D compressible Euler equation with the damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu <1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions exist globally…

Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…

In this paper, we consider exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove global existence of smooth solutions. Similar to the constant coefficients case, we show…

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…