On the Majorana condition for nonlinear Dirac systems

TL;DR

This paper proves global existence and scattering for nonlinear Dirac systems with large initial data satisfying an approximate Majorana condition, in critical three-dimensional spaces.

Contribution

It establishes the first global well-posedness and scattering results for large data in nonlinear Dirac equations under an approximate Majorana condition.

Findings

Global existence for large initial data

Scattering results in critical spaces

Applicable to Dirac with Soler-type nonlinearity and Dirac-Klein-Gordon system

Abstract

For arbitrarily large initial data in an open set defined by an approximate Majorana condition, global existence and scattering results for solutions to the Dirac equation with Soler-type nonlinearity and the Dirac-Klein-Gordon system in critical spaces in spatial dimension three are established.