论文标题
紧凑型谎言组的非线性分数波方程
Nonlinear fractional wave equation on compact Lie groups
论文作者
论文摘要
让$ g $成为一个紧凑的谎言组。在本文中，我们考虑了$ g $上具有功率类型非线性的初始值分数方程。主要是，我们研究了一些$ l^{2} -l^{2} $在$ g $上的组傅立叶变换的帮助下，$ g $的均质分数波方程的解决方案的估计值。此外，使用对紧凑型谎言组的傅立叶分析，我们证明了局部时间的存在导致能量空间。此外，在初始数据的某些条件下，建立了有限的时间爆破结果。我们还为局部（及时）解决方案提供了急剧的寿命。最后，我们考虑具有常规质量项的空间折叠方程，具体取决于位置，并研究紧凑型谎言组上分数klein-gordon方程的适当性。
Let $G$ be a compact Lie group. In this article, we consider the initial value fractional wave equation with power-type nonlinearity on $G$. Mainly, we investigate some $L^{2}-L^{2}$ estimates of the solutions to the homogeneous fractional wave equation on $G$ with the help of the group Fourier transform on $G$. Further, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space. Moreover, under certain conditions on the initial data, a finite time blow-up result is established. We also derive a sharp lifespan for local (in-time) solutions. Finally, we consider the space-fractional wave equation with a regular mass term depending on the position and study the well-posedness of the fractional Klein-Gordon equation on compact Lie groups.
