Global solution to nonlinear Dirac equation for Gross-Neveu model in $1+1$ dimensions

TL;DR

This paper proves the global existence and uniqueness of strong solutions for a class of nonlinear Dirac equations in 1+1 dimensions, including models like the Gross-Neveu and Thirring models, under bounded initial data.

Contribution

It establishes the first rigorous proof of global well-posedness for these nonlinear Dirac equations with cubic terms in 1+1 dimensions.

Findings

Global existence of solutions proved

Uniqueness of solutions established

Applicable to models like Gross-Neveu and Thirring

Abstract

This paper studies a class of nonlinear Dirac equations with cubic terms in $R^{1+1}$, which include the equations for the massive Thirring model and the massive Gross-Neveu model. Under the assumption that the initial data has bounded $L^2$ norm, the global existence and the uniqueness of the strong solution in $C([0,\infty),L^2(R^1))$ are proved.