Modulation Spaces and Applications to Hartree-Fock equations

We discuss some progress of the last decade (and ongoing interest) of modulation spaces from the PDE point of view. We prove some local and global well-posedness for Hartree- Fock equations in modulation spaces. We shall also prove similar results when a harmonic potential is added to these equations.
This is a joint work with Manoussos Grillakis and Kasso Okoudjou.