English

On Blowup for time-dependent generalized Hartree-Fock equations

Analysis of PDEs 2011-11-30 v1 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0909.3043,
  title  = {On Blowup for time-dependent generalized Hartree-Fock equations},
  author = {Christian Hainzl and Enno Lenzmann and Mathieu Lewin and Benjamin Schlein},
  journal= {arXiv preprint arXiv:0909.3043},
  year   = {2011}
}

Comments

24 pages

R2 v1 2026-06-21T13:47:10.414Z