Blow-up for a stochastic model of chemotaxis driven by conservative noise on $\mathbb{R}^2$ - Centre de mathématiques appliquées (CMAP)
Article Dans Une Revue Journal of Evolution Equations Année : 2023

Blow-up for a stochastic model of chemotaxis driven by conservative noise on $\mathbb{R}^2$

Résumé

Abstract We establish criteria on the chemotactic sensitivity $\chi $ for the non-existence of global weak solutions (i.e., blow-up in finite time) to a stochastic Keller–Segel model with spatially inhomogeneous, conservative noise on $\mathbb{R}^2$. We show that if $\chi$ is sufficiently large then 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 $\chi $ in an intermediate regime, determined by the variance of the initial data and the spatial correlation of the noise, we show that blow-up occurs with positive probability.
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hal-04191089 , version 1 (09-09-2024)

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Avi Mayorcas, Milica Tomašević. Blow-up for a stochastic model of chemotaxis driven by conservative noise on $\mathbb{R}^2$. Journal of Evolution Equations, 2023, 23, pp.57. ⟨10.1007/s00028-023-00900-3⟩. ⟨hal-04191089⟩
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