Global strong solution to a nonlinear Dirac type equation in one dimension

TL;DR

This paper proves the global existence and decay of solutions for a class of nonlinear massless Dirac equations in one dimension, including models like Thirring and Gross-Neveu, under small initial charge conditions.

Contribution

It establishes the global strong solution existence and decay properties for nonlinear massless Dirac equations in one dimension, a novel result for these models.

Findings

Global strong solutions exist under small charge assumptions.

Decay of local charge is demonstrated.

Includes models like massless Thirring and Gross-Neveu.

Abstract

This paper studies a class of nonlinear massless Dirac equations in one dimension, which include the equations for massless Thirring model and massless Gross-Neveu model. Under the assumptions that the initial data has small charge and is bounded, the global existence of the strong solution is established. The decay of the local charge is also proved.