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arXiv · 2308.15287

Enhanced dissipation and blow-up suppression for the three dimensional Keller-Segel equation with a non-shear incompressible flow

Binbin Shi·Weike Wang
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Abstract

In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with a large non-shear incompressible flow. Without advection, there exist solution with arbitrarily mass which blow up in finite time. Firstly, we introduce a three dimensional non-shear incompressible flow and study the enhanced dissipation of such flows by resolvent estimate method. Next, we show that the enhanced dissipation of such flow can suppress blow-up of solution to three dimensional parabolic-elliptic Keller-Segel equation and establish global classical solution with large initial data.

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Binbin Shi, Weike Wang. 2023-08-29. Enhanced dissipation and blow-up suppression for the three dimensional Keller-Segel equation with a non-shear incompressible flow. https://arxiv.org/abs/2308.15287

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