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Stability problem in the dust-Einstein system with a positive cosmological constant - Oxbridge PDE Days

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  • User Dr Mahir Hadžić - King's College London
  • ClockThursday 20 March 2014, 11:00-12:00
  • HouseMR2.

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The dust-Einstein system models the evolution of a spacetime containing a pressureless fluid, i.e. dust. We will show nonlinear stability of the well-known Friedman-Lemaitre-Robertson-Walker (FLRW) family of solutions to the dust-Einstein system with positive cosmological constant. FLRW solutions represent initially a quiet fluid evolving in a spacetime undergoing accelerated expansion. We work in a harmonic-type coordinate system, inspired by prior works of Rodnianski and Speck on Euler-Einstein system, and Ringstroem’s work on the Einstein-scalar-field system. The main new mathematical difficulty is the additional loss of one degree of differentiability of the dust matter. To deal with this degeneracy, we commute the equations with a well-chosen differential operator and derive a family of elliptic estimates to complement the high-order energy estimates. This is joint work with Jared Speck.

http://www.maths.cam.ac.uk/postgrad/cca/oxbridgepde2014.html

This talk is part of the Cambridge Centre for Analysis talks series.

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