Smooth solution for incompressible Navier–Stokes equations with large initial

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.

Keywords:

• Incompressible Navier–Stokes equations
• global solutions
• large initial data

MSC:

• 35A01
• 35B45
• 35E15
• 35Q30

Acknowledgments

The author is grateful for the warm hospitality.

Disclosure statement

No potential conflict of interest was reported by the author(s).