Abstract
In this paper, I shall construct a family of global smooth solutions with large initial data for the incompressible Navier–Stokes equations, which are allowed to have a large three-dimensional part and a small three-dimensional part. In addition, one also acquires a global well-posedness with low regular data to the incompressible Navier–Stokes equations.
Acknowledgments
The author is grateful for the warm hospitality.
Disclosure statement
No potential conflict of interest was reported by the author(s).