Global Existence for The Massive Dirac Equations with small initial datum on Tori

TL;DR

This paper proves almost global and global existence results for the massive Dirac equations on tori with small initial data, using advanced analytical estimates.

Contribution

It introduces new global existence results for Dirac equations on tori with both high and low regularity initial data, employing Gagliardo-Nirenberg-Moser and Bernstein-type estimates.

Findings

Almost global existence for high regularity initial data.

Global existence for low regularity initial data.

Use of Gagliardo-Nirenberg-Moser and Bernstein-Type Lemma in proofs.

Abstract

In the article we obtain almost global existence for Dirac Equations with high regularity and small initial datum on Tori. Besides, the global existence with low regularity and small initial datum is gotten. The approaches are mainly Gagliardo-Nirenberg-Moser estimates and Bernstein-Type Lemma.