# Chao Liu: Stability of FLRW metric for polytropic (Makino) fluids

**Time: **
Tue 2019-12-03 10.00 - 11.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan

**Lecturer: **
Chao Liu, Peking University

### Abstract

We establish the future non-linear stability of de Sitter-like Friedmann-Lemaître-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with polytropic fluids (the proof can also allow more general Makino fluids containning certain nonlinear or linear equations of state). We emphasize for polytropic fluids, this stability problem is not a trival generalization of the previous known results (the difficulties mainly come from the Euler equation and the nonlinear equation of state can offset some effects of positive cosmological constant). Our method is based on the Fuchsian formulations. This is a joint work with Changhua Wei.