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

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.