Large time behavior for the incompressible Navier–Stokes flows in 2D exterior domains

Abstract

The incompressible Navier–Stokes flows in a 2D exterior domain are considered, for which the associated total net force to the boundary may not vanish. The decay properties are shown for the first and second derivatives of the Navier–Stokes flows in L1 and weighted spaces, respectively, which improve Theorem 1.2 in Bae and Jin (J Funct Anal 240:508–529, 2006).