Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation

Binbin Shi; Weike Wang

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arXiv · 1908.02489

Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation

Binbin Shi·Weike Wang

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Abstract

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.

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Binbin Shi, Weike Wang. 2019-08-07. Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation. https://arxiv.org/abs/1908.02489

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