Local existence and uniqueness for the frictional Newton-Schroedinger equation in three dimensions

Abstract

We prove local existence and uniqueness for the Newton-Schroedinger equation in three dimensions. Further we show that the blow-up alternative holds true as well as the continuous dependence of the solution w.r.t. the initial data.

References in corpus (3)

• Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
• The one-dimensional Schrödinger-Newton equations
• The frictional Schrödinger-Newton equation in models of wave function collapse