On Blowup for time-dependent generalized Hartree-Fock equations

Details On Blowup for time-dependent generalized Hartree-Fock equations On Blowup for time-dependent generalized Hartree-Fock equations

2009-09-16

arxiv.org/abs/0909.3043v1

Ann. Henri Poincar\'e 11 (2010), no. 6, 1023-1052

Mathematics

Analysis of PDEs

24 pages

Scientific paper

10.1007/s00023-010-0054-3

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.

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