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Remark on 3-D Navier-Stokes system with strong dissipation in one direction

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The second author is supported by NSF of China under Grants 11688101 and 11371347, and innovation grant from National Center for Mathematics and Interdisciplinary Sciences

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  • 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].

    Mathematics Subject Classification: Primary: 35Q30, 76D03.


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