Bilinear Estimates and Applications to Global Well-posedness for the Dirac-Klein-Gordon Equation on R^{1+1}

Details Bilinear Estimates and Applications to Global Well-posedness for the Dirac-Klein-Gordon Equation on R^{1+1} Bilinear Estimates and Applications to Global Well-posedness for the Dirac-Klein-Gordon Equation on R^{1+1}

2012-02-09

arxiv.org/abs/1202.1967v1

Mathematics

Analysis of PDEs

27 pages, 1 figure

Scientific paper

We prove new bilinear estimates for the X^{s, b}_\pm(R^2) spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on R^{1+1}. The proof of the bilinear estimates follows from a dyadic decomposition in the spirit of Tao [21] and D'Ancona, Foschi, and Selberg [11]. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka, and Tao, we extend the work of Tesfahun [23] on global existence below the charge class for the Dirac-Klein- Gordon equation on R^{1+1}.

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