In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with fractional dissipation and the additional mixing effect of advection by an incompressible flow. Under suitable mixing condition on the advection, we study well-posedness of solution with large initial data. We establish the global $L^\infty$ estimate of the solution through nonlinear maximum principle, and obtain the global classical solution.

中文翻译：

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通过在具有分数耗散的广义 Keller-Segel 系统中混合来抑制爆炸

在本文中，我们考虑了具有分数耗散的广义抛物线椭圆 Keller-Segel 方程的柯西问题和不可压缩流对流的附加混合效应。在合适的平流混合条件下，我们研究了具有大量初始数据的解的适定性。我们通过非线性极大值原理建立解的全局$L^\infty$估计，得到全局经典解。