Global well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficient

摘要

In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data. Then we shall construct a family of initial data, u(0,nu) which vary fast enough in the vertical variable and which can be arbitrarily large in the space BMO-1. Yet u(0,nu) still generates a unique global solution to the classical 3-D Navier-Stokes system provided that nu is sufficiently large. (C) 2020 Elsevier Inc. All rights reserved.