Abstract
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, u0,ν, which vary fast enough in the vertical variable and which can be arbitrarily large in the space BMO−1. Yet u0,ν still generates a unique global solution to the classical 3-D Navier-Stokes system provided that ν is sufficiently large.
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