Small data scattering for a cubic Dirac equation with Hartree type\n nonlinearity in R¹⁺³

2017/10/22 by Achenef Tesfahun, Tesfahun, Achenef · 1 citation
Mathematics · #35Q55 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1710.07919

openalex publication_date 2017/10/22 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

We prove that the initial value problem for the Dirac equation\n \n ( -i\γ^\μ \∂_\μ + m \) \ψ\n = \( frace^{- |x|}|x| \∗ ( \ψ \ψ)\) \ψ \n∈ R¹⁺³ \n is globally well-posed and the solution scatters to free waves asymptotically\nas t \→ \± \∞, if we start with initial data that is small in\nH^s for s>0. This is an almost critical well-posedness result in the sense\nthat L² is the critical space for the equation. The main ingredients in the\nproof are Strichartz estimates, space-time bilinear null-form estimates for\nfree waves in L², and an application of the U^p and V^p-function spaces.\n

Cited by

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

Related

• Scattering results for Dirac Hartree-type equations with small initial data
• Small data scattering of 2d Hartree type Dirac equations
• Scattering and non-scattering of the Hartree-type nonlinear Dirac system at critical regularity
• Improved multilinear estimates and global regularity for general nonlinear wave equations in (1+3) dimensions
• Conditional large-data global well-posedness of Dirac equation with Hartree-type nonlinearity