Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system

Details Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system

2007-03-08

arxiv.org/abs/math/0703220v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be locally well-posed for low regularity Dirac data in $\hat{H^{s,p}}$ and wave data in $\hat{H^{r,p}} \times \hat{H^{r-1,p}}$ for $1^s \hat{f}\|_{L^{p'}}$, generalizing the results for $p=2$ by Selberg and Tesfahun. Especially we are able to improve the results from the scaling point of view with respect to the Dirac part.

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