Smoothing estimates for variable coefficients Schroedinger equation with electromagnetic potentials

TL;DR

This paper develops multiplier techniques to establish virial identities and smoothing estimates for electromagnetic variable coefficient Schrödinger equations, advancing understanding of their behavior under perturbations.

Contribution

It introduces a novel application of multiplier methods to derive smoothing estimates for Schrödinger equations with electromagnetic potentials and variable coefficients.

Findings

Established virial identities for the equation.

Proved smoothing estimates in a perturbative setting.

Extended classical techniques to variable coefficient electromagnetic cases.

Abstract

In this paper we develop the classical multiplier technique to prove a virial identity and smoothing estimates (in a perturbative setting) for the electromagnetic variable coefficients Schroedinger equation.