- Series
- PDE Seminar
- Time
- Tuesday, April 2, 2013 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Mahir Hadzic – MIT
- Organizer
- Zhiwu Lin
We study small perturbations of the well-known
Friedman-Lemaitre-Robertson-Walker (FLRW) solutions to the dust-Einstein
system with a positive cosmological constant on a spatially periodic
background. These solutions model a quiet fluid in a spacetime undergoing
accelerated expansion. We show that the FLRW solutions are nonlinearly
globally future-stable under small perturbations of their initial data. Our
result extends the stability results of Rodnianski and Speck for the
Euler-Einstein system with positive cosmological constant to the case of
dust (i.e. a pressureless fluid). The main difficulty that we overcome is
the degenerate nature of the dust model that loses one degree of
differentiability with respect to the Euler case. To resolve it, we commute
the equations with a well-chosen differential operator and develop a new
family of elliptic estimates that complement the energy estimates. This is
joint work with J. Speck.