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arXiv · 2111.02245

Blow-up for a Stochastic Model of Chemotaxis Driven by Conservative Noise on $\mathbb{R}^2$

Avi Mayorcas·Milica Tomasevic
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Abstract

We establish criteria on the chemotactic sensitivity $χ$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on $\mathbb{R}^2$. We show that if $χ$ is sufficiently large then \emph{blow-up} occurs with probability $1$. In this regime our criterion agrees with that of a deterministic Keller--Segel model with increased viscosity. However, for $χ$ in an intermediate regime, determined by the variance of the initial data and the spatial correlation of the noise, we show that \emph{blow-up} occurs with positive probability.

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Avi Mayorcas, Milica Tomasevic. 2023-08-31. Blow-up for a Stochastic Model of Chemotaxis Driven by Conservative Noise on $\mathbb{R}^2$. https://doi.org/10.1007/s00028-023-00900-3

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