ar X iv : m at h - ph / 0 60 80 20 v 1 7 A ug 2 00 6 DYNAMICAL COLLAPSE OF WHITE DWARFS IN HARTREE - AND HARTREE - FOCK THEORY

We study finite-time blow-up for pseudo-relativistic Hartreeand Hartree-Fock equations, which are model equations for the dynamical evolution of white dwarfs. In particular, we prove that radially symmetric initial configurations with negative energy lead to finite-time blow-up of solutions. Furthermore, we derive a mass concentration estimate for radial blow-up solutions. Both results are mathematically rigorous and are in accordance with Chandrasekhar’s physical theory of white dwarfs, stating that stellar configurations beyond a certain limiting mass lead to “gravitational collapse” of these objects. Apart from studying blow-up, we also prove local well-posedness of the initial-value problem for the Hartreeand Hartree-Fock equations underlying our analysis, as well as global-in-time existence of solutions with sufficiently small initial data, corresponding to white dwarfs whose stellar mass is below the Chandrasekhar limit.