Abstract
We completely determine the range of Sobolev regularity for the Maxwell--Dirac system in $1+1$ space time dimensions to be well-posed locally in the case that the initial data of the Dirac part regularity is of $L^2$. The well-posedness follows from the standard energy estimates. Outside the range for the well-posedness, we show either the flow map is not continuous or not twice differentiable at zero.
Citation
Mamoru Okamoto. "Well-posedness and ill-posedness of the Cauchy problem for the Maxwell-Dirac system in $1+1$ space time dimensions." Adv. Differential Equations 18 (1/2) 179 - 199, January/February 2013. https://doi.org/10.57262/ade/1355867485
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