This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and the external force. Based on the Schauder’s fixed point theorem, we establish the sufficient conditions for the existence and uniqueness of the global mild solution in Banach spaces. Moreover, the polynomial decay estimate of the mild solution is given. Furthermore, the approximate controllability for the mild solution is obtained by constructing a Cauchy sequence.

中文翻译：

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时滞分数阶Navier-Stokes方程的温和解的近似可控性

本文讨论了对流项和外力中存在时滞的分数阶Navier-Stokes方程的温和解的一些结果。基于Schauder不动点定理，我们为Banach空间中整体温和解的存在和唯一性建立了充分条件。此外，给出了温和解的多项式衰减估计。此外，通过构建柯西序列获得了对温和溶液的近似可控性。