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Global strong solution to the Thirring model in critical space. (English) Zbl 1218.81077
Summary: We obtain a strong solution in charge critical space ${L}^{2}\left(ℝ\right)$ 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 ${\Psi }\in {L}^{\infty }\left(\left[0,T\right];{L}^{2}\left(ℝ\right)\cap {L}^{4}\left(ℝ\right)\right)$. A decay of local charge and asymptotic behavior of the field can be shown directly.
##### MSC:
 81T10 Model quantum field theories 81U15 Exactly and quasi-solvable systems (quantum theory) 81Q80 Special quantum systems, such as solvable systems
##### References:
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