Global existence of solutions to the Cauchy problem for time‐dependent Hartree equations

Global existence of solutions to the Cauchy problem for time‐dependent Hartree equations

The existence of global solutions to the Cauchy problem for time‐dependent Hartree equations for N electrons is established. The solution is shown to have a uniformly bounded H 1(R3) norm and to satisfy an estimate of the form ∥ ψ (t) ∥ H 2 ⩽ c exp(k t). It is shown that ’’negative energy’’ solution...

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Veröffentlicht in:J. Math. Phys. (N.Y.), v. 16, no. 5, pp. 1122-1130 v. 16, no. 5, pp. 1122-1130, 1975-05, Vol.16 (5), p.1122-1130
Hauptverfasser: Chadam, J. M., Glassey, R. T.
Format: Artikel
Sprache:eng
Schlagworte:
CAUCHY PROBLEM- HARTREE-FOCK METHOD
ELECTRONS
ENERGY
N76100 -Physics (Theoretical)-General
TIME DEPENDENCE
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Zusammenfassung:The existence of global solutions to the Cauchy problem for time‐dependent Hartree equations for N electrons is established. The solution is shown to have a uniformly bounded H 1(R3) norm and to satisfy an estimate of the form ∥ ψ (t) ∥ H 2 ⩽ c exp(k t). It is shown that ’’negative energy’’ solutions do not converge uniformly to zero as t → ∞.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.522642