Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
- 1 May 1975
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 16 (5) , 1122-1130
- https://doi.org/10.1063/1.522642
Abstract
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 H1(R3) norm and to satisfy an estimate of the form ∥ ψ (t) ∥H2 ⩽ c exp(kt). It is shown that ’’negative energy’’ solutions do not converge uniformly to zero as t → ∞.Keywords
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