Global Well-posedness of the 1D Dirac-Klein-Gordon system in Sobolev spaces of negative index

Details Global Well-posedness of the 1D Dirac-Klein-Gordon system in Sobolev spaces of negative index Global Well-posedness of the 1D Dirac-Klein-Gordon system in Sobolev spaces of negative index

2008-09-06

arxiv.org/abs/0809.1164v1

Mathematics

Analysis of PDEs

26 pages, 1 figure

Scientific paper

We prove that the Cauchy problem for the Dirac-Klein-Gordon system of equations in 1D is globally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor and positive index for the scalar field. The main ingredient in the proof is the theory of almost conservation law and I-method introduced by Colliander, Keel, Staffilani, Takaoka and Tao. Our proof also relies on the null structure in the system, and bilinear spacetime estimates of Klainerman-Machedon type.

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