This paper deals with the logistic Keller–Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters χ, κ ∈ ℝ and μ > 0), and shows that any nonnegative initial data (u0, v0) ∈ L1 × W1,2 lead to global solutions that are smooth in $\bar {\Omega }\times (0,\infty )$.

中文翻译：

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具有二维逻辑项的 Keller-Segel 系统中 L1 × W1,2 中初始数据的即时平滑和全局解决方案

本文处理逻辑 Keller-Segel 模型\[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{例} \]在有界二维域中（具有齐次 Neumann 边界条件和参数 χ，κ∈ ℝ 和μ> 0)，并表明任何非负初始数据 (你0,v0) ∈大号1×W1,2导致顺利进行的全球解决方案$\bar {\Omega }\times (0,\infty )$.