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20170419Nonlinear stability of Minkowski space-time with massive scalar field
20170419Nonlinear stability of Minkowski space-time with massive scalar field
教师介绍

本讲教师:马跃
所属学科:理科
人  气:303

课程介绍
Abstract: In this talk we will present some recent work about the system of Einstein equation coupled with a massive scalar field (partially published in [2]). More precisely, on the nonlinear global stability of the Minkowski space-time. In a PDE point of view, this is equivalent to theglobal existence of a special class of quasi-linear wave-Klein-Gordon system with small initial data. The wave-Klein-Gordon system, due to its lack of scaling invariance and its lack of Klein-Gordon structure, can not be treated by a simple combination of the classical techniques applied on wave equations and Klein-Gordon equations. To solve this difficulty, we introduced the “hyperboloidal foliation method” introduced by the author in [1] combined with some newly developed tools such as L∞ estimates on Klein-Gordon equations in curved space-time and L∞ estimates on wave equations based on the expression of spherical means. We also adapt some tools developed in classical framework for the analysis of Einstein equation into our hyperboloidal foliation framework, such as the estimates based on wave gauge conditions and the L∞ estimates on wave equations based on integration along characteristics. References [1] P. LeFloch and Y. MA The hyperboloidal foliation method, World Scientific, 2015 [2] P. LeFloch and Y. MA The nonlinear stablity of Minkowski space for self-gratitating massive field. The wave-Klein-Gordon model, Communications in Mathematical Physics September 2016, Volume 346, Issue 2, pp 603-665

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