Global strong solution to the Thirring model in critical space

We obtain a strong solution in charge critical space L2(R) of the Thirring system and Federbusch equations in one space dimension by using solution representation of the models. The uniqueness is obtained for the solution Ψ∈L∞([0,T];L2(R)∩L4(R)). A decay of local charge and asymptotic behavior of the field can be shown directly.