Variable potentials and dispersive equations

TL;DR

This paper establishes Strichartz estimates for Schrödinger equations with time-dependent potentials that can have infinite total variation, broadening the class of potentials for which dispersive estimates are valid.

Contribution

It introduces new Strichartz estimates applicable to Schrödinger equations with highly irregular, non-integrable time-dependent potentials.

Findings

Strichartz estimates hold for potentials with infinite total variation

The results extend dispersive analysis to more general time-dependent potentials

Potential applications in quantum dynamics with irregular external fields

Abstract

We prove Strichartz-type estimates for Schroedinger's equation with time-dependent potentials. The time derivative of the potentials need not be integrable, so the total variation of the potentials may be infinite.