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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

Nikolaos Bournaveas 1,

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.
Keywords: restriction method., Klainerman null forms.
Mathematics Subject Classification: Primary: 35L70; Secondary: 35Q4.
Citation: Nikolaos Bournaveas. Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 605-616. doi: 10.3934/dcds.2008.20.605
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