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