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Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension

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  • We study a nonlinear Dirac system in one space dimension with a quadratic nonlinearity which exhibits null structure in the sense of Klainerman. Using an $L^{p}$ variant of the $L^2$ restriction method of Bourgain and Klainerman-Machedon, we prove local well-posedness for initial data in a Sobolev-like space $\hat{H^{s,p}}(\R)$ whose scaling dimension is arbitrarily close to the critical scaling dimension.
    Mathematics Subject Classification: Primary: 35L70; Secondary: 35Q40.


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