This paper studies the stability of a stationary solution of the Navier–Stokes system in $3$-D exterior domains. The stationary solution is called a Leray's stationary solution if the Dirichlet integral is finite. We apply an energy inequality and maximal $L^p$-in-time regularity for Hilbert space-valued functions to derive the decay rate with respect to time of energy solutions to a perturbed Navier–Stokes system governing a Leray's stationary solution.
Hajime KOBA. "On stability of Leray's stationary solutions of the Navier–Stokes system in exterior domains." J. Math. Soc. Japan 69 (1) 373 - 396, January, 2017. https://doi.org/10.2969/jmsj/06910373