Conditional large-data global well-posedness of Dirac equation with Hartree-type nonlinearity

Abstract

We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential in two and three spatial dimensions. This paper improves our previous results [7,6]; we establish global well-posedness and scattering for large data with a certain condition. Firstly we investigate the long-time behavior of solutions to the Dirac equation satisfies good control provided that a particular dispersive norm of solutions is bounded. The key of our proof relies on modifying multilinear estimates obtained in our previous papers.Secondly, we obtain large data scattering by exploiting the Majorana condition.

Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality

“…The condition (1.2) was observed in [4,8] for the equations with identity matrix in place of γ 5 . It is regarded as a perturbation of Majorana condition studied in [17,5,18].…”