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

Hartmut Pecher
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Abstract

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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Hartmut Pecher. 2007-03-08. Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system. https://arxiv.org/abs/math/0703220

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