Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 497 - 505
Well-posedness of the Cauchy problem for the Maxwell–Dirac system in one space dimension
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.
Received: 16 December 2011
Revised: 7 February 2012
First available in Project Euclid: 30 October 2018
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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