Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows
Abstract
We study Keller--Segel systems on $ \mathbb{T}\times\mathbb{R}$ subject to a stochastic Couette transport flow. We prove that sufficiently strong mixing suppresses chemotactic finite-time blow-up with high probability; thus yielding a unique global-in-time mild solution for initial data of arbitrary mass. Moreover, we obtain a quantitative estimate for the probability of blow-up, showing that it decays exponentially with increasing strength of the stochastic shear. Our analysis is based on the enhanced dissipation generated by the stochastic shear flow. To prove our main result, we first construct a maximal local mild solution through pathwise estimates for the random solution operator of passive scalar transport equations and a fixed-point argument. To obtain global control, we decompose the evolution into time blocks and exploit mixing-induced decay of the nonzero spatial Fourier modes. A nonlinear bootstrap argument then yields global existence above an almost-sure finite random threshold for the shear strength which is obtained by an application of the Borel-Cantelli theorem.
Related
- Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
- Identifying secondary critical mass levels in two- and higher-dimensional Keller-Segel systems
- Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric α-stable process
- Blow-up suppression for the 2D parabolic-parabolic Patlak-Keller-Segel-Navier-Stokes system
- Well-posedness of 2D stochastic parabolic-parabolic Keller-Segel system with logistic source
BibTeX
@misc{kong2026suppression,
title = {{Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows}},
author = {Fanze Kong and Krutika Tawri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25551},
eprint = {2609.25551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25551},
}
RIS
TY - UNPB
TI - Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows
AU - Fanze Kong
AU - Krutika Tawri
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.25551
UR - https://arxiv.org/abs/2609.25551
AB - We study Keller--Segel systems on $ \mathbb{T}\times\mathbb{R}$ subject to a stochastic Couette transport flow. We prove that sufficiently strong mixing suppresses chemotactic finite-time blow-up with high probability; thus yielding a unique global-in-time mild solution for initial data of arbitrary mass. Moreover, we obtain a quantitative estimate for the probability of blow-up, showing that it decays exponentially with increasing strength of the stochastic shear. Our analysis is based on the enhanced dissipation generated by the stochastic shear flow. To prove our main result, we first construct a maximal local mild solution through pathwise estimates for the random solution operator of passive scalar transport equations and a fixed-point argument. To obtain global control, we decompose the evolution into time blocks and exploit mixing-induced decay of the nonzero spatial Fourier modes. A nonlinear bootstrap argument then yields global existence above an almost-sure finite random threshold for the shear strength which is obtained by an application of the Borel-Cantelli theorem.
ER -