A Note on Global Existence for the Chemotaxis–Stokes Model with Nonlinear Diffusion

This note is concerned with the Cauchy problem on the 3D chemotaxis–Stokes equations with nonlinear diffusions and large initial data. We prove the global existence of weak solutions for all adiabatic exponents ⁠. In particular, the result fills up the gap between m=1 by Winkler [24] and by Liu and Lorz [16]. A similar result also holds for the 2D chemotaxis–Navier–Stokes equations.