Abstract
In this paper, we consider the stability of the Couette flow for the Cauchy problem to the parabolic-parabolic chemotaxis-Navier–Stokes system in T×R, we prove that the Couette flow is stable under the extra smallness assumption, where the amplitude is large enough. This result was inspired by Zeng et al. (2021), they investigated the suppression of blow-up in Patlak–Keller–Segel-Navier–Stokes system via the Couette flow. Compared with their work, our chemical equation has different nonlinear term, which leads to the difficulty of estimates of chemical gradient.
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