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Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows
We study Keller--Segel systems on $\mathbb R^2$ advected by a stochastic Couette flow. We prove that sufficiently strong mixing suppresses chemotactic blow-up almost surely, yielding a unique global mild solution for initial data of arbitrary mass. To prove this result, we construct maximal local mi
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