# Meeting Details

Title: Instability theory of gaseous stars CCMA PDEs and Numerical Methods Seminar Series Ian Tice, Carnegie Mellon University http://www.math.cmu.edu/math/faculty/Tice A simple astrophysical model of stars considers them to be a compact mass of self-gravitating compressible fluid. Such a fluid obeys the compressible Navier-Stokes-Poisson equations. In the case of "polytropic gases," in which the pressure behaves like $P = K \rho^\gamma$ for $K>0$ an entropy constant and $\gamma >1$ an adiabatic constant, one may construct compactly supported, finite mass, radially symmetric equilibrium solutions by reducing to the Lane-Emden ODE (at least when $6/5 < \gamma < 2$). A fundamental question in astrophysics is the stability of such equilibria, and it was believed that they should be unstable for $6/5 < \gamma < 4/3$ and stable for $4/3 \le \gamma < 2$. In this talk we will prove that the Navier-Stokes-Poisson system, perturbed around a Lane-Emden equilibrium configuration, is nonlinearly unstable when $6/5 < \gamma < 4/3$. This is joint work with Juhi Jang.