Magnetic virial identities, weak dispersion and Strichartz inequalities

TL;DR

This paper develops virial identities for Schrödinger and wave equations with electromagnetic potentials, leading to weak dispersive inequalities and Strichartz estimates under specific conditions.

Contribution

It introduces new virial identities and applies them to establish Strichartz inequalities for wave equations with electromagnetic potentials.

Findings

Established weak dispersive inequalities in dimensions n≥3.

Proved Strichartz inequalities for wave equations with non-trapping electromagnetic potentials.

Derived Morawetz and smoothing estimates for Schrödinger and wave equations.

Abstract

We show a family of virial-type identities for the Schr\"odinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dimension $n\geq3$, involving Morawetz and smoothing estimates, are proved; finally, we apply them to prove Strichartz inequalities for the wave equation with a non-trapping electromagnetic potential with almost Coulomb decay.