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

Yanlin Liu; Ping Zhang

doi:10.3934/cpaa.2020244

Article Contents

2021, Volume 20, Issue 7&8: 2765-2787. Doi: 10.3934/cpaa.2020244

This issue Previous Article On the invariant region for compressible Euler equations with a general equation of state Next Article Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system

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

Yanlin Liu^1, and
Ping Zhang^2, ,

1.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

^* Corresponding author
^* Corresponding author

Received: April 2020

Revised: July 2020

Early access: September 2020

Published: August 2021

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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Abstract

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].

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

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References

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