Mild solutions to the Cauchy problem for time-space fractional Keller-Segel-Navier-Stokes system

2022/09/25 by Z. Jiang, Lei Wang, Jiang, Z. +1
Mathematics · #35A01 #35C06 #35Q35 #35Q92 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.12171

openalex publication_date 2022/09/25 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

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.

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