2022/05/22 by Zhao, Zhiwen
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.2205.10776
openalex publication_date 2022/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a mathematical model of two adjacent rigid particles immersed into a viscous incompressible fluid is considered. The main feature of the flow is that the Cauchy stress tensor consisting of the strain tensor and the pressure will appear blow-up as the distance between these two particles tends to zero. For the purpose of making clear this high concentration, a family of unified stress concentration factors are precisely captured in all dimensions, which determine whether the Cauchy stress tensor will blow up or not. As a direct application, we establish optimal gradient estimates and asymptotics of the Cauchy stress tensor for Stokes flow, which indicate that its maximal singularity comes from the pressure.