Annales Henri Poincaré

, Volume 11, Issue 6, pp 1023–1052 | Cite as

On Blowup for Time-Dependent Generalized Hartree–Fock Equations

  • Christian Hainzl
  • Enno LenzmannEmail author
  • Mathieu Lewin
  • Benjamin Schlein


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.


Angular Momentum Hartree Equation Bogoliubov Theory Symmetric Initial Data Type Evolution Equation 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Christian Hainzl
    • 1
  • Enno Lenzmann
    • 2
    Email author
  • Mathieu Lewin
    • 3
  • Benjamin Schlein
    • 4
  1. 1.Department of MathematicsUABBirminghamUSA
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagen ØDenmark
  3. 3.CNRS & Laboratoire de Mathématiques, (CNRS UMR 8088)Université de Cergy-PontoiseCergy-PontoiseFrance
  4. 4.Institute for Applied MathematicsUniversity of BonnBonnGermany

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