Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows

Autor:	He, Siming
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.06048 Zobrazit plný text záznamu View this record from Arxiv