一个修正的最小作用原理，允许早期宇宙重建问题的质量集中

Q4 Mathematics

Confluentes Mathematici Pub Date : 2011-11-20 DOI:10.1142/S1793744211000400

Y. Brenier

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引用次数: 18

摘要

我们解决了早期宇宙重建(EUR)问题(如Frisch及其合作者在[26]中所考虑的)，以及相关的Zeldovich近似模型[46]。通过用完全非线性的蒙日-安培方程代替线性泊松方程来模拟引力，我们引入了一个修正的数学模型(“蒙日-安培引力/MAG”)，该模型的Zeldovich近似变得精确。MAG模型具有最小作用原理，其中我们可以以一种规范的方式输入质量浓度效应，该原理基于具有凸势的梯度流理论，并与Ghoussoub[29]提出的自对偶拉格朗日概念有一定关系。针对一维空间的EUR问题，提出了一种全离散算法。

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A MODIFIED LEAST ACTION PRINCIPLE ALLOWING MASS CONCENTRATIONS FOR THE EARLY UNIVERSE RECONSTRUCTION PROBLEM

We address the early universe reconstruction (EUR) problem (as considered by Frisch and coauthors in [26]), and the related Zeldovich approximate model [46]. By substituting the fully nonlinear Monge–Ampere equation for the linear Poisson equation to model gravitation, we introduce a modified mathematical model ("Monge-Ampere gravitation/MAG"), for which the Zeldovich approximation becomes exact. The MAG model enjoys a least action principle in which we can input mass concentration effects in a canonical way, based on the theory of gradient flows with convex potentials and somewhat related to the concept of self-dual Lagrangians developed by Ghoussoub [29]. A fully discrete algorithm is introduced for the EUR problem in one space dimension.

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.