Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space

Abstract

We study the initial value problem of some nonlinear Dirac equations which are $L^m\left(ℝ\right)$ critical. Corresponding to the structure of nonlinear terms, global strong solutions can be obtained in different Lebesgue spaces by using solution representation formula. The uniqueness of weak solutions is proved for the solution $U\in L^{\infty }\left(\left[0,T\right]; Y^{m+2}\left(ℝ\right)\right)$.