Dynamical Collapse of White Dwarfs in Hartree- and Hartree-Fock Theory |
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Authors: | Jürg Fröhlich Enno Lenzmann |
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Affiliation: | 1.Institute for Theoretical Physics,ETH Zürich–H?nggerberg,Zürich,Switzerland;2.Department of Mathematics,Massachusetts Institute of Technology,Cambridge,USA |
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Abstract: | 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. |
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