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VOL. 64 | 2015 Well-posedness of the Cauchy problem for the Maxwell–Dirac system in one space dimension
Mamoru Okamoto

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

## Abstract

We determine the range of Sobolev regularity for the Maxwell–Dirac system in $1+1$ space time dimensions to be well-posed locally. The well-posedness follows from the null form estimates. Outside the range for the well-posedness, we show either the flow map is not continuous or not twice differentiable at zero.

## Information

Published: 1 January 2015
First available in Project Euclid: 30 October 2018

zbMATH: 1335.35212
MathSciNet: MR3381317

Digital Object Identifier: 10.2969/aspm/06410497

Subjects:
Primary: 35L70, 35Q40