Global strong solution to the Thirring model in critical space

We obtain a strong solution in charge critical space L 2 ( 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 ] ; L 2 ( R ) ∩ L 4 ( R ) ) . A decay of local charge and asymptotic behavior of the field can be shown directly.