For a 2D chemotaxis-Navier-Stokes system with singular sensitivity up to c^{-5/6}, global bounded weak solutions exist under mild diffusion growth and bounded initial oxygen; if gamma > 1/2, initial bacterial mass must also be bounded.
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Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier--Stokes system
For a 2D chemotaxis-Navier-Stokes system with singular sensitivity up to c^{-5/6}, global bounded weak solutions exist under mild diffusion growth and bounded initial oxygen; if gamma > 1/2, initial bacterial mass must also be bounded.