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arXiv · 1202.1967

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

Timothy Candy
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Abstract

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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Timothy Candy. 2012-02-09. Bilinear Estimates and Applications to Global Well-posedness for the Dirac-Klein-Gordon Equation on R^{1+1}. https://arxiv.org/abs/1202.1967

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