Mathematics – Mathematical Physics
Scientific paper
Sep 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cmaph.274..737s&link_type=abstract
Communications in Mathematical Physics, Volume 274, Issue 3, pp.737-750
Mathematics
Mathematical Physics
5
Plate, Periodic Heat Conduction, Heat Exchanger Surfaces, Convection
Scientific paper
We study finite-time blow-up for pseudo-relativistic Hartree- and 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 Hartree- and 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.
Georgiou Demos P.
Siakavellas Nicolaos J.
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