Global well-posedness for the massless cubic Dirac equation

Nikolaos Bournaveas, Timothy Candy

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the cubic Dirac equation with zero mass is globally well posed for small data in the scale invariant space ˙Hn−12(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.
Original languageEnglish
Pages (from-to)6735-6828
Number of pages94
JournalInternational Mathematics Research Notices
Volume2016
Issue number22
Early online date23 Dec 2015
DOIs
Publication statusPublished - Nov 2016

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