On the cubic Dirac equation with potential and the Lochak--Majorana condition

2017/06/19 by Piero DʼAncona, Mamoru Okamoto, D'Ancona, Piero +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1706.06479

openalex publication_date 2017/06/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We study a cubic Dirac equation on ℝ×ℝ³ i ∂ _t u + D u + V(x) u = ⟨ βu,u ⟩ βu perturbed by a large potential with almost critical regularity. We prove global existence and scattering for small initial data in H¹ with additional angular regularity. The main tool is an endpoint Strichartz estimate for the perturbed Dirac flow. In particular, the result covers the case of spherically symmetric data with small H¹ norm. When the potential V has a suitable structure, we prove global existence and scattering for large initial data having a small chiral component, related to the Lochak--Majorana condition.

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