Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension

Details Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension

2006-11-23

arxiv.org/abs/math/0611718v1

Mathematics

Analysis of PDEs

Scientific paper

We extend recent results of S. Machihara and H. Pecher on low regularity well-posedness of the Dirac-Klein-Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain-Klainerman-Machedon spaces.

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