Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（6）
• 页码范围: 1175-1204
• 页数: 30页
• 语种: 英文

摘要

We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables.In particular,when one of these viscous coefficients is large enough compared with the initial data,we prove the global well-posedness of this system.In fact,we obtain the existence of a global strong solution to (NS) when the initial data verifies an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.