In this paper, we investigate the fast signal diffusion limit of solutions of the fully parabolic Keller–Segel–Stokes system to solution of the parabolic–elliptic-fluid counterpart in a two-dimensional or three-dimensional bounded domain with smooth boundary. Under the natural volume-filling assumption, we establish an algebraic convergence rate of the fast signal diffusion limit for general large initial data by developing a series of subtle bootstrap arguments for combinational functionals and using some maximal regularities. In our current setting, in particular, we can remove the restriction to asserting convergence only along some subsequence in Wang–Winkler and the second author (Cal. Var., 2019).

中文翻译：

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具有大初始数据的 Keller-Segel-Stokes 系统的快速信号扩散极限的收敛速度

在本文中，我们研究了在具有平滑边界的二维或三维有界域中，完全抛物线 Keller-Segel-Stokes 系统解对抛物线-椭圆流体对应解的快速信号扩散极限。在自然体积填充假设下，我们通过为组合泛函开发一系列微妙的自举参数并使用一些最大规则，为一般大初始数据建立快速信号扩散极限的代数收敛速度。特别是在我们当前的设置中，我们可以消除对仅沿着 Wang-Winkler 和第二作者（Cal. Var.，2019）的某些子序列断言收敛的限制。