Maxwell-Klein-Gordon系统在Fourier-Lebesgue空间数据下的近最优局部适定性
偏微分方程分析
2019-11-12 v3
摘要
我们证明了三维空间中Maxwell-Klein-Gordon系统在Fourier-Lebesgue空间\widehat{H}^{s,r}中数据的低正则性局部适定性结果，其中\|f\|_{\widehat{H}^{s,r}} = \|\langle \xi \rangle^s \widehat{f}(\xi)\|_{\widehat{L}^{r'}}，\frac{1}{r}+\frac{1}{r'} = 1。所假设的数据正则性在r → 1时相对于缩放几乎是最优的。这弥合了已知r=2情形（即s > 3/4）与相对于缩放的临界值s_c = 1/2之间的差距。
引用
@article{arxiv.1908.05651,
title = {Almost optimal local well-posedness for the Maxwell-Klein-Gordon system with data in Fourier-Lebesgue spaces},
author = {Hartmut Pecher},
journal= {arXiv preprint arXiv:1908.05651},
year = {2019}
}
备注
18 pages, slightly modified version according to the suggestions of the referee, to appear in Comm. Pure Appl. Analysis