On blowup for time-dependent generalized Hartree-Fock equations

TY - JOUR

T1 - On blowup for time-dependent generalized Hartree-Fock equations

AU - Hainzl, Christian

AU - Lenzmann, Enno

AU - Lewin, Mathieu

AU - Schlein, Benjamin

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

U2 - 10.1007/s00023-010-0054-3

DO - 10.1007/s00023-010-0054-3

M3 - Journal article

SN - 1424-0637

VL - 11

SP - 1023

EP - 1052

JO - Annales Henri Poincare

JF - Annales Henri Poincare

ER -