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March/April 2010 Low regularity well-posedness for some nonlinear Dirac equations in one space dimension
Sigmund Selberg, Achenef Tesfahun
Differential Integral Equations 23(3/4): 265-278 (March/April 2010).

Abstract

We prove that the Cauchy problem for a nonlinear Dirac equation with vector self-interaction (Thirring model) and for a nonlinear system of two Dirac equations coupled through a vector-vector interaction (Federbusch model) are locally well posed, in one space dimension, for initial data in Sobolev spaces of almost critical dimension; i.e., in $H^\varepsilon$, the critical space being $L^2$, and globally well posed for initial data in $H^{1/2+\varepsilon}$, for any $\varepsilon>0$. We also consider a nonlinear Dirac equation with quadratic nonlinearity which was studied earlier by S.~Machihara and N.~Bournaveas. We prove that the Cauchy problem for this equation is locally well posed for initial data in $H^{\varepsilon}$.

Citation

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Sigmund Selberg. Achenef Tesfahun. "Low regularity well-posedness for some nonlinear Dirac equations in one space dimension." Differential Integral Equations 23 (3/4) 265 - 278, March/April 2010.

Information

Published: March/April 2010
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35362
MathSciNet: MR2588476

Subjects:
Primary: 35L70, 35Q40

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.23 • No. 3/4 • March/April 2010
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