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July  2008, 20(3): 605-616. doi: 10.3934/dcds.2008.20.605

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

 1 University of Edinburgh, School of Mathematics, Edinburgh EH9 3JZ, United Kingdom

Received  October 2006 Revised  October 2007 Published  December 2007

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.
Citation: Nikolaos Bournaveas. Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 605-616. doi: 10.3934/dcds.2008.20.605
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