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

Research paper by Achenef Tesfahun

Indexed on: 06 Sep '08Published on: 06 Sep '08Published in: Mathematics - Analysis of PDEs



Abstract

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.