## Advanced Studies in Pure Mathematics

### Well-posedness of the Cauchy problem for the Maxwell–Dirac system in one space dimension

Mamoru Okamoto

#### 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.

#### Article information

Dates
Revised: 7 February 2012
First available in Project Euclid: 30 October 2018

https://projecteuclid.org/ euclid.aspm/1540934248

Digital Object Identifier
doi:10.2969/aspm/06410497

Mathematical Reviews number (MathSciNet)
MR3381317

Zentralblatt MATH identifier
1335.35212

#### Citation

Okamoto, Mamoru. Well-posedness of the Cauchy problem for the Maxwell–Dirac system in one space dimension. Nonlinear Dynamics in Partial Differential Equations, 497--505, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410497. https://projecteuclid.org/euclid.aspm/1540934248