Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field

Sigmund Selberg

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arXiv · 1707.02719

Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field

Sigmund Selberg

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Abstract

We prove global well-posedness for the coupled Maxwell-Dirac-Thirring-Gross-Neveu equations in one space dimension, with data for the Dirac spinor in the critical space $L^2(\R)$. In particular, we recover earlier results of Candy and Huh for the Thirring and Gross-Neveu models, respectively, without the coupling to the electromagnetic field, but the function spaces we introduce allow for a greatly simplified proof. We also apply our method to prove local well-posedness in $L^2(\R)$ for a quadratic Dirac equation, improving an earlier result of Tesfahun and the author.

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Sigmund Selberg. 2017-07-10. Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field. https://arxiv.org/abs/1707.02719

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