%0 Journal Article
%T On Blowup for time-dependent generalized Hartree-Fock equations
%A Christian Hainzl
%A Enno Lenzmann
%A Mathieu Lewin
%A Benjamin Schlein
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s00023-010-0054-3
%X 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.
%U http://arxiv.org/abs/0909.3043v1