Global Existence of the Critical Einstein-Equivariant Wave Map System

临界爱因斯坦等变波图系统的整体存在性

• 批准号: 262621851
• 负责人: Dr. Nishanth Gudapati
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/262621851?language=en
• 关键词: Global; Existence; Critical; Einstein; Equivariant

A fundamental and interesting aspect of mathematics is that it provides a consistent language for expressing our understanding of the phenomena occurring in nature. An example is the wave equation which models many natural phenomena like vibrating strings, acoustic waves, water waves, electromagnetic waves and linearized Einstein's equations of general relativity. A geometric and nonlinear generalization of the wave equation is the wave maps equation. The motivation to study wave maps is that they occur naturally in Einstein's equations of general relativity and are proven tools to understand the nonlinear effects of Einstein's equations.The aim of the proposed project is to prove global existence of equivariant wave maps coupled to Einsteins equations of general relativity. The proposed techniques for the proof are based on Friedlander's representation formula and its recent improvements by Vincent Moncrief. In addition to introducing new techniques in the study of nonlinear wave equations, the project has implications for one of the fundamental questions in general relativity: the global regularity of Einstein's equations and consequently the cosmic censorship conjectures of Roger Penrose.

数学的一个基本而有趣的方面是，它提供了一种一致的语言来表达我们对自然界中发生的现象的理解。一个例子是波动方程，它模拟了许多自然现象，如振动的弦，声波，水波，电磁波和线性化的爱因斯坦广义相对论方程。波动方程的几何和非线性推广是波动映射方程。研究波映射的动机是它们自然地出现在爱因斯坦的广义相对论方程中，并且被证明是理解爱因斯坦方程的非线性效应的工具。拟议项目的目的是证明与爱因斯坦广义相对论方程耦合的等变波映射的整体存在性。所提出的证明技术是基于Friedlander的表示公式和Vincent Moncrief最近的改进。除了在非线性波动方程的研究中引入新技术外，该项目还涉及广义相对论的一个基本问题：爱因斯坦方程的全局正则性以及罗杰·彭罗斯的宇宙审查理论。

项目成果

On Scattering for Small Data of $$\varvec{2 + 1}$$2+1-Dimensional Equivariant Einstein-Wave Map System

关于$$varvec{2 1}$$2一维等变爱因斯坦波图系统小数据的散射

• DOI: 10.1007/s00023-017-0599-5
• 发表时间: 2017
• 期刊: Annales Henri Poincaré
• 作者: Nishanth Gudapati;B. Dodson
• 通讯作者: B. Dodson

Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System

• DOI: 10.1007/s40818-017-0030-z
• 发表时间: 2015-01
• 期刊: Annals of PDE
• 影响因子: 2.8
• 作者: L. Andersson;N. Gudapati;J. Szeftel