GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX

Achenef Tesfahun

Type: Article

Publication Date: 2009-09-01

Citations: 16

DOI: https://doi.org/10.1142/s0219891609001952

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 space–time estimates of Klainerman–Machedon type.

Locations

Journal of Hyperbolic Differential Equations - View
arXiv (Cornell University) - View - PDF

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