On Dirac equations with Hartree type nonlinearity in modulation spaces

TL;DR

This paper establishes local well-posedness for Dirac equations with Hartree nonlinearity in modulation spaces, broadening the class of initial data that can be analyzed.

Contribution

It introduces a novel approach to handle initial data in modulation spaces, extending previous results on Dirac equations with Hartree nonlinearity.

Findings

Proves local well-posedness in modulation spaces.

Extends initial data class beyond previous studies.

Provides a new analytical framework for Dirac equations.

Abstract

We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not addressed in previous studies.