The Hartree–Fock equations in modulation spaces

Abstract

We establish both a local and a global well-posedness theories for the nonlinear Hartree–Fock equations and its reduced analog in the setting of the modulation spaces on In addition, we prove similar results when a harmonic potential is added to the equations. In the process, we prove the boundedeness of certain multilinear operators on products of the modulation spaces which may be of independent interest.