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