Bournaveas, Nikolaos Local well-posedness for a nonlinear Dirac equation in spaces of almost critical dimension. (English) Zbl 1144.35306 Discrete Contin. Dyn. Syst. 20, No. 3, 605-616 (2008). Summary: 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 \(\widehat{H^{s,p}(\mathbb{R})}\) whose scaling dimension is arbitrarily close to the critical scaling dimension. Cited in 12 Documents MSC: 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) 35L70 Second-order nonlinear hyperbolic equations 35Q40 PDEs in connection with quantum mechanics 35B33 Critical exponents in context of PDEs Keywords:Klainerman null forms; restriction method; null structure PDFBibTeX XMLCite \textit{N. Bournaveas}, Discrete Contin. Dyn. Syst. 20, No. 3, 605--616 (2008; Zbl 1144.35306) Full Text: DOI