On stability of physically reasonable solutions to the two-dimensional Navier-Stokes equations

The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 R. Finn and D. R. Smith proved the unique existence of stationary solutions, called the physically reasonable solutions, to the Navier-Stokes equations in a two-dimensional exterior domain that describe this type of flows when the Reynolds number is sufficiently small. The asymptotic behavior of their solutions at spatial infinity has been studied in details and well understood by now, while its stability has been open due to the difficulty specific to the two-dimensionality. In this talk we show that the physically reasonable solutions constructed by Finn and Smith are asymptotically stable with respect to small and well-localized initial perturbations.