In this paper, we investigate the Cauchy problem for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. By taking advantage of a coupling structure of the equations and using a scale decomposition technique, we explore a new estimate of solutions. This estimate together with a microlocal analysis entails the global existence and uniqueness of weak solutions to the chemotaxis-Navier--Stokes system for a large class of initial data.
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Zhang et al. (2014) studied this question.
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