On the Decay in the Energy Space of Solutions to the Damped Magnetic Radial Schrödinger Equation with Non-Local Nonlinearities

Abstract

We will explore, in any space dimension d≥4, the decay in the energy space for the damped magnetic Schrödinger equation with non-local nonlinearity and radial initial data in H1(Rd). We will also display new Morawetz identities and corresponding localized Morawetz estimates.

Keywords

• nonlinear Schrödinger equations
• Schrödinger operators
• scattering theory
• non-local nonlinearity
• damping