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SUMMARY:Stability problem in the dust-Einstein system with a positive cosm
 ological constant - Oxbridge PDE Days -  Dr Mahir Hadžić - King's Colleg
 e London
DTSTART:20140320T110000Z
DTEND:20140320T120000Z
UID:TALK51568@talks.cam.ac.uk
CONTACT:36127
DESCRIPTION:The dust-Einstein system models the evolution of a spacetime c
 ontaining a pressureless fluid\, i.e. dust. We will show nonlinear stabili
 ty of the well-known Friedman-Lemaitre-Robertson-Walker (FLRW) family of s
 olutions to the dust-Einstein system with positive cosmological constant. 
 FLRW solutions represent initially a quiet fluid evolving in a spacetime u
 ndergoing accelerated expansion. We work in a harmonic-type coordinate sys
 tem\, inspired by prior works of Rodnianski and Speck on Euler-Einstein sy
 stem\, and Ringstroem's work on the Einstein-scalar-field system. The main
  new mathematical difficulty is the additional loss of one degree of diffe
 rentiability of the dust matter. To deal with this degeneracy\, we commute
  the equations with a well-chosen differential operator and derive a famil
 y of elliptic estimates to complement the high-order energy estimates. Thi
 s is joint work with Jared Speck.\n\nhttp://www.maths.cam.ac.uk/postgrad/c
 ca/oxbridgepde2014.html
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