On Blowup for Time-Dependent Generalized Hartree-Fock Equations

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. 287:705-714, 2009) 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.