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

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.

11pages, submitted

References in corpus (2)

• Block-diagonalization of the linearized coupled-mode system
• Survey on global existence in the nonlinear Dirac equations in one dimension

Cited by in corpus (6)

• Orbital stability of Dirac solitons
• Integrable semi-discretization of the massive Thirring system in laboratory coordinates
• Global solution to a cubic nonlinear Dirac equation in 1+1 dimensions
• Global solution to nonlinear Dirac equation for Gross-Neveu model in $1+1$ dimensions
• Initial boundary value problem for nonlinear Dirac equation of Gross-Neveu type in $1+1$ dimensions
• Large time behavior of solution to nonlinear Dirac equation in $1+1$ dimensions