On stability of Leray's stationary solutions of the Navier–Stokes system in exterior domains

Abstract

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.