Open AccessRemark on 3-D Navier-Stokes system with strong dissipation in one direction
Author(s) -
Yanlin Liu,
Ping Zhang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2020244
Subject(s) - vorticity , mathematics , norm (philosophy) , dissipation , compressibility , mathematical analysis , anisotropy , physics , vortex , mechanics , law , quantum mechanics , political science
In this paper, we consider 3D anisotropic incompressible Navier-Stokes equations with strong dissipation in the vertical direction. We shall prove that this system has a unique global strong solution and the norm of the vertical component of the velocity field can be controlled by the norm of the corresponding component to the initial data. Similar result can also be obtained for the horizontal components of the vorticity. In particular, we simplify our proofs to the well-posedness result in our previous paper [ 11 , 13 ].