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.

我们建立了趋化敏感性标准\(\chi \)，以证明随机 Keller-Segel 模型不存在全局弱解（即有限时间内的爆炸），该模型在\(\mathbb上具有空间不均匀、保守的噪声{R}^2\)。我们证明，如果\(\chi \)足够大，则爆炸发生的概率为 1。在这种情况下，我们的标准与粘度增加的确定性 Keller-Segel 模型的标准一致。然而，对于中间状态下的\(\chi \)来说，由初始数据的方差和噪声的空间相关性决定，我们表明爆炸发生的概率为正。