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arXiv · 1910.03972

Local well-posedness of the two-dimensional Dirac-Klein-Gordon equations in Fourier-Lebesgue spaces

Hartmut Pecher
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Abstract

The local well-posedness problem is considered for the Dirac-Klein-Gordon system in two space dimensions for data in Fourier-Lebesgue spaces $\hat{H}^{s,r}$ , where $\|f\|_{\hat{H}^{s,r}} = \| \langle \xi \rangle^s \hat{f}\|_{L^{r'}}$ and $r$ and $r'$ denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d'Ancona, Foschi and Selberg in the classical case $r=2$ . Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.

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Hartmut Pecher. 2019-10-09. Local well-posedness of the two-dimensional Dirac-Klein-Gordon equations in Fourier-Lebesgue spaces. https://arxiv.org/abs/1910.03972

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