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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^ estimate of the solution through nonlinear maximum principle, and obtain the global classical solution.
Shi et al. (Wed,) studied this question.