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SUMMARY:Einstein equation coupled with positive mass scalar field\, global
 -in-time existence - Yue Ma\, Xi’an Jiaotong University
DTSTART:20160118T150000Z
DTEND:20160118T160000Z
UID:TALK63637@talks.cam.ac.uk
CONTACT:Amit Einav
DESCRIPTION:In this Talk we will discuss the system of Einstein equation c
 oupled with a positive mass scalar field. The problem to be solved is the 
 stability of the Minkowski vacuum or\, in another word\, the global-in-tim
 e existence of the regular solution associated to a small\, regular initia
 l data.\nContrary to the existent result which concentrated mainly on the 
 vacuum case or coupling with mass-zero filed\, our case leads to a system 
 of coupled wave-Klein-Gordon system. For this\, we apply the hyperboloidal
  foliation method that we have recently developed specifically on this kin
 d of system. But due to the complexity of the problem\, we also developed 
 new techniques including the $L^\\infty - L^\\infty$ estimates of Klein-Go
 rdon equation in curved space-time\, the $L^\\infty - L^\\infty$ estimate 
 on wave equations based on spherical-mean expression. We also re-state the
  existent techniques in the hyperboloidal foliation framework such as the 
 integration along characteristics\, the decomposition of quasi-null terms 
 and the estimates based on wave coordinate conditions.
LOCATION:CMS\, MR13
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