scholarly journals The Cauchy Problem for the Einstein Equations

1999 ◽  
pp. 127-223 ◽  
Author(s):  
Helmut Friedrich ◽  
Alan Rendall
Keyword(s):  
Cauchy Problem ◽  
Einstein Equations ◽  
The Cauchy Problem

Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations

1990 ◽  
Vol 427 (1872) ◽  
pp. 221-239 ◽  
Keyword(s):  
Cauchy Problem ◽  
Perfect Fluid ◽  
Initial Value Problem ◽  
Einstein Equations ◽  
Initial Value ◽  
Fluid Source ◽  
Null Hypersurfaces ◽  
The Cauchy Problem ◽  
Well Posed ◽  
Characteristic Initial Value Problem

A method is described by means of which the characteristic initial value problem can be reduced to the Cauchy problem and examples are given of how it can be used in practice. As an application it is shown that the characteristic initial value problem for the Einstein equations in vacuum or with perfect fluid source is well posed when data are given on two transversely intersecting null hypersurfaces. A new discussion is given of the freely specifiable data for this problem.

Karl Stellmacher 1938, the Cauchy problem for the Einstein equations

2012 ◽  
pp. 15-39
Author(s):  
Andrzej Krasiński ◽  
George F. R. Ellis ◽  
Malcolm A. H. MacCallum
Keyword(s):  
Cauchy Problem ◽  
Einstein Equations ◽  
The Cauchy Problem

scholarly journals On Classical Global Solutions of Nonlinear Wave Equations with Large Data

2017 ◽  
Vol 2019 (19) ◽  
pp. 5859-5913 ◽  
Author(s):  
Shuang Miao ◽  
Long Pei ◽  
Pin Yu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Wave Equations ◽  
Global Solutions ◽  
Large Data ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Classical Solutions ◽  
Linear Wave ◽  
The Cauchy Problem

Abstract This article 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 energy. The choice of the large Cauchy initial data is inspired by Christodoulou's characteristic initial data in his work [2] on formation of black holes. The main innovation of the current work is that we discovered a relaxed energy ansatz which allows us to prove decay-in-time-estimate. Therefore, the new estimates can also be applied in studying the Cauchy problem for Einstein equations.

scholarly journals The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions

2011 ◽  
Vol 12 (3) ◽  
pp. 419-482 ◽  
Author(s):  
Yvonne Choquet-Bruhat ◽  
Piotr T. Chruściel ◽  
José M. Martín-García
Keyword(s):  
Cauchy Problem ◽  
Einstein Equations ◽  
Characteristic Cone ◽  
The Cauchy Problem ◽  
Arbitrary Dimensions

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

Sign in / Sign up

Export Citation Format

Share Document