报告题目：Suppression of blow-up in Patlak-Keller-Segel system coupled with linearized Navier-Stokes equations via the 3D Couette flow
报告人：王莉莉 博士
工作单位：大连理工大学
报告时间：2024年07月09日 10:00-12:00
报告地点：数信学院 305
报告摘要：
It is known that finite-time blow-up in the 3D Patlak-Keller-Segel system may occur for arbitrarily small value of the initial mass. It's interesting whether one can prevent the finite-time blow-up via the stabilizing effect of the moving fluid. Consider the three-dimensional Patlak-Keller-Segel system coupled with the linearized Navier-Stokes equations near the Couette flow (𝑨𝒚,𝟎,𝟎)in a finite channel 𝑻×I×𝑻 with 𝑻=[𝟎,𝟐𝝅) and 𝑰=[−𝟏,𝟏], with the non-slip boundary condition, and we show that if the shear flow is sufficiently strong (𝑨 is large enough), then the solutions toPatlak-Keller-Segel-Navier-Stokes system are global in time as long as the initial cell mass is sufficiently small (for example, 𝑴<𝟒/𝟗) and 𝑨(〖||𝒖〗_(𝟐,𝟎) (𝟎)||_(𝑳^𝟐 )+〖||𝒖〗_(𝟑,𝟎) (𝟎)||_(𝑳^𝟐 ) )≤𝑪_𝟎, which seems to be the first result of considering the suppression effect of Couette flow in the 3D Patlak-Keller-Segel-Navier-Stokes model.
This is a joint work with Shikun Cui and Wendong Wang.
报告人简介：
王莉莉，博士研究生。数学与信息科学学院杰出校友，现就读于大连理工大学数学科学学院，师从王文栋教授。研究主要集中于非线性偏微分方程领域，具体包括Navier-Stokes方程、趋化模型等流体方程的稳定性和正则性问题。
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