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SUMMARY:Non linear stability of Minkowski space-time with massive scalar f
ield
DTSTART;VALUE=DATE-TIME:20160617T101000Z
DTEND;VALUE=DATE-TIME:20160617T104500Z
DTSTAMP;VALUE=DATE-TIME:20200716T180122Z
UID:indico-contribution-2970@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yue Ma (School of Mathematics and Statistics)\nIn th
is talk we will present some recent work about the system of Einstein equa
tion coupled with a massive scalar field and the system of $f(R)$ field eq
uation (partially published in [2]). More precisely\, on the nonlinear glo
bal stability of the Minkowski space-time within these two similar context
s. In a PDE point of view\, they are equivalent to the global existence of
a special class of quasi-linear wave-Klein-Gordon system with small initi
al data.\n\nTo the author’s knowledge there is not so much choice to dea
l with this kind of system (for a detailed explication of the major diffic
ulty\, see for example in [1] page 2)\, and we apply the “hyperboloidal
foliation method” introduced by the author in [1] combined with some new
ly developed tools such as $L^∞$ estimates on Klein-Gordon equations in
curved space-time and $L^∞$ estimates on wave equations based on the exp
ression of spherical means. We also adapt some tools developed in classica
l framework for the analysis of Einstein equation into our hyperboloidal f
oliation framework\, such as the estimates based on wave gauge conditions
and the L$^∞$ estimates on wave equations based on integration along cha
racteristics.\n\n\nReferences\n\n[1] P. LeFloch and Y. Ma\, The hyperboloi
dal foliation method\, World Scientific\, 2015\n\n[2] P. LeFloch and Y. Ma
\, The nonlinear stability of Minkowski space for self-gravitating massive
field. The\nwave-Klein-Gordon model\, Comm. Math. Phys.\, published onlin
e.\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2970/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2970/
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