We construct solutions to the two-dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time T. The solution is decomposed as the sum of a stationary state concentrated at scale λ and of a perturbation. We rely on a detailed spectral analysis for the linearised dynamics in the parabolic neighbourhood of the singularity performed by the authors in [10], providing a refined expansion of the perturbation. Our main result is the construction of a stable dynamics in the full nonradial setting for which the stationary state collapses with the universal law

中文翻译：

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2D Keller-Segel 系统奇异解的改进描述和稳定性

我们构建了二维抛物线椭圆 Keller-Segel 模型的解决方案，用于在有限时间T内爆炸的趋化性。解被分解为集中在尺度λ的静止状态和扰动的总和。我们依赖于作者在 [10] 中对奇点抛物线邻域中的线性化动力学进行的详细光谱分析，从而提供了对扰动的精细扩展。我们的主要结果是在完全非径向设置中构建了一个稳定的动力学，其中静止状态随普遍规律崩溃