Global well-posedness for the massless cubic Dirac equation

2014/07/02 by Nikolaos Bournaveas, Bournaveas, Nikolaos, Timothy Candy +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1407.0655

openalex publication_date 2014/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the cubic Dirac equation with zero mass is globally well-posed for small data in the scale invariant space H^(n-1)/(2)(Rⁿ) for n=2, 3. The proof proceeds by using the Fierz identities to rewrite the equation in a form where the null structure of the system is readily apparent. This null structure is then exploited via bilinear estimates in spaces based on the null frame spaces of Tataru. We hope that the spaces and estimates used here can be applied to other nonlinear Dirac equations in the scale invariant setting. Our work complements recent results of Bejenaru-Herr who proved a similar result for n=3 in the massive case.

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• Global solutions to cubic Dirac and Dirac-Klein-Gordon systems on spacetimes close to the Minkowski space

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