2020/06/30 by Oliver Sieber, Sieber, Oliver
Engineering · Mathematics · #35Q35 #35Q92 #76A15 #76D03 #76D05 #82C31 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2006.16832
openalex publication_date 2020/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider an inhomogeneous Doi model which was introduced by W. E and P. Zhang [Meth. Appl. of Anal., 13 (2006), pp. 181 - 198]. We extend their model, which couples a Smoluchowski equation to a Navier-Stokes type equation, for active particles by introducing an additional stress tensor. Exploiting the energetic and entropic structure of the system, we establish the existence of global-in-time weak solutions in two and three space dimensions for both passive and active particles. In particular, our result holds for minimal regularity assumptions on the initial data and without restrictions on the Reynolds and Deborah number.