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arXiv · 0903.3189

Global solutions for the Dirac-Klein-Gordon system in two space dimensions

Axel Gruenrock·Hartmut Pecher
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Abstract

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth (classical) solution. The proof uses function spaces of Bourgain type based on Besov spaces - previously applied by Colliander, Kenig and Staffilani for generalized Benjamin-Ono equations and also by Bejenaru, Herr, Holmer and Tataru for the 2D Zakharov system - and the null structure of the system detected by d'Ancona, Foschi and Selberg, and a refined bilinear Strichartz estimate due to Selberg. The global existence proof uses an idea of Colliander, Holmer and Tzirakis for the 1D Zakharov system.

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Axel Gruenrock, Hartmut Pecher. 2009-06-22. Global solutions for the Dirac-Klein-Gordon system in two space dimensions. https://arxiv.org/abs/0903.3189

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