Anisotropically weighted Lq$L^q$‐Lr$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier–Stokes flow past a rigid body

Abstract

AbstractWe consider the spatial–temporal behavior of the Navier–Stokes flow past a rigid body in . This paper develops analysis in Lebesgue spaces with anisotropic weights , which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the x1‐direction. We derive anisotropically weighted ‐ estimates for the Oseen semigroup in exterior domains. As applications of those estimates, we study the stability/attainability of the Navier–Stokes flow in anisotropically weighted spaces to get the spatial–temporal behavior of nonstationary solutions.