Enhanced dissipation and blow-up suppression for the three dimensional Keller-Segel equation with the plane Couette-Poiseuille flow

In this paper, we consider the Cauchy problem for the three dimensional parabolic -elliptic Keller -Segel equation with the large plane Couette-Poiseuille flow. Without advection, there exist solution with arbitrarily mass which blow up in finite time. Firstly, we introduce three dimensional plane Couette-Poiseuille flow and study the enhanced dissipation effect of such flows by resolvent estimate method. Next, we show that the enhanced dissipation effect of such flows can suppress blow-up of solution to three dimensional parabolicelliptic Keller -Segel equation and establish global classical solution with large initial data. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.