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January/February 2013 Well-posedness and ill-posedness of the Cauchy problem for the Maxwell-Dirac system in $1+1$ space time dimensions
Mamoru Okamoto
Adv. Differential Equations 18(1/2): 179-199 (January/February 2013).

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

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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.

Information

Published: January/February 2013
First available in Project Euclid: 18 December 2012

zbMATH: 1261.35126
MathSciNet: MR3052714

Subjects:
Primary: 35L70 , 35Q40

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 1/2 • January/February 2013
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