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.
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.
基金
supported by the Agence Nationale de la Recherche, Project IFSMACS (Grant No. ANR-15-CE40-0010)
supported by National Natural Science Foundation of China (Grant Nos. 11371347 and 11688101)
Morningside Center of Mathematics of the Chinese Academy of Sciences and Innovation Grant from National Center for Mathematics and Interdisciplinary Sciences
