We discuss some ongoing interest (since last decade) in use of modulation spaces in harmonic analysis and its connection to nonlinear dispersive equations. In particular, we shall discuss results on Hermite multiplier and composition operators on modulation spaces. As an application to these, we shall point out that nonlinear Schro¨dinger equation (NLS) is locally wellposed in modulation spaces for the power-type nonlinearity u|u|α (α ∈ 2N), and the standard method for the evolution of NLS cannot be considered for nonlinearity of the form u|u|α,α ∈ (0,∞)\2N.
Finally, we will discuss the state of the art to establish global wellposedness for the Hartree-Fock equations of ﬁnite particles in modulation spaces. We shall also discuss similar results when harmonic potential is added to the equations.
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Meeting ID: 943 3476 0957