论文标题
凯奇问题的轻度解决方案，用于时间空间的分数凯勒 - 塞格 - 纳维尔 - 塞托克斯系统
Mild solutions to the Cauchy problem for time-space fractional Keller-Segel-Navier-Stokes system
论文作者
论文摘要
本文调查了时间间隔分数Keller-Segel-Navier- Stokes模型的凯奇问题，该模型可以描述系统的记忆效应和Lévy过程。 Lebesgue空间中的局部存在和全局存在分别通过Banach固定点定理和Banach隐式函数定理获得。此外，在均匀的Sobolev空间中，局部和全球温和解决方案的规律得到了改善。此外，还建立了温和解决方案的某些特性，包括质量保护，衰减估计值，稳定性和自相似性。
This paper investigates the Cauchy problem of the time-space fractional Keller-Segel-Navier- Stokes model, which can describe both memory effect and Lévy process of the system. The local existence and global existence in Lebesgue space are obtained by means of Banach fixed point theorem and Banach implicit function theorem, respectively. In addition, the regularities of local and global mild solutions are improved in fractional homogeneous Sobolev spaces. Furthermore, some properties of mild solutions including mass conservation, decay estimates, stability and self-similarity are established.
