Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Hartmut Pecher

Institution:	1. Fachbereich Mathematik und Naturwissenschaften, Bergische Universit?t Wuppertal, Gau?str. 20, 42097, Wuppertal, Germany

Abstract:	The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be locally well-posed for low regularity Dirac data in $\widehat{H^{s,p}}$ and wave data in $\widehat{H^{r,p}} \times {H^{\widehat{r-1},p}}$ for $1< p \leq 2$ under certain assumptions on the parameters r and s, where $\\|f\\|_{\widehat{H^{s,p}}} := \\| \langle \xi \rangle^{s} \hat{f}\\|_{L^{p^{\prime}}}$ , 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.

Keywords:	:" target="_blank">: Dirac – Klein – Gordon system well-posedness Fourier restriction norm method
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