相关论文: Global characteristic problem for Einstein vacuum …
This is the second part of our result on a class of global characteristic problems for the Einstein vacuum equations with small initial data. In the previous work denoted by (I), our attention was focused on prescribing the initial data…
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…
The goal of this article is to parametrise solutions to Einstein's equations with big bang singularities and quiescent asymptotics. To this end, we introduce a notion of initial data on big bang singularities and conjecture that it can be…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future complete null cone with suitable decay, and show that the solution exists uniformly around the null cone for general such…
Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy…
In this note, we show that the conical solution-operator method of Mao-Tao in [Localized initial data for Einstein equations] applies to a simple construction of vacuum asymptotically flat initial data at minimal and borderline decay…
Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…
We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is…
This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…
In this paper we introduce the characteristic gluing problem for the Einstein vacuum equations. We present a codimension-$10$ gluing construction for characteristic initial data which are close to the Minkowski data and we show that the…
In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…
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…
We prove the global existence of solution to the small data mass critical stochastic nonlinear Schr\"{o}dinger equation in $d=1$. We further show the stability of the solution under perturbation of initial data. Our construction starts with…
We make use of an improved existence result for the characteristic initial value problem for the conformal Einstein equations to show that given initial data on two null hypersurfaces $\mathcal{N}_\star$ and $\mathcal{N}'_\star$ such that…
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…