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Volume 38, Issue 1
Global Solutions of 3-D Inhomogeneous Navier-Stokes System with Large Viscosity in One Variable

Tiantian Hao

DOI: 10.4208/cmr.2021-0040

Commun. Math. Res., 38 (2022), pp. 62-80.

Published online: 2021-11

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  • Abstract

We consider the global well-posedness of three dimensional incompressible inhomogeneous Navier-Stokes equation 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 and the initial density is close enough to a positive constant, we prove the global well-posedness of this system. This result extends the previous results in [9, 11] for the classical Navier-Stokes system.

  • Keywords

Inhomogeneous Navier-Stokes system, anisotropic Littlewood-Paley theory, global well-posedness.

  • AMS Subject Headings

35Q30, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-62, author = {Hao , Tiantian}, title = {Global Solutions of 3-D Inhomogeneous Navier-Stokes System with Large Viscosity in One Variable}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {38}, number = {1}, pages = {62--80}, abstract = {

We consider the global well-posedness of three dimensional incompressible inhomogeneous Navier-Stokes equation 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 and the initial density is close enough to a positive constant, we prove the global well-posedness of this system. This result extends the previous results in [9, 11] for the classical Navier-Stokes system.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0040}, url = {http://global-sci.org/intro/article_detail/cmr/19957.html} }
TY - JOUR T1 - Global Solutions of 3-D Inhomogeneous Navier-Stokes System with Large Viscosity in One Variable AU - Hao , Tiantian JO - Communications in Mathematical Research VL - 1 SP - 62 EP - 80 PY - 2021 DA - 2021/11 SN - 38 DO - http://doi.org/10.4208/cmr.2021-0040 UR - https://global-sci.org/intro/article_detail/cmr/19957.html KW - Inhomogeneous Navier-Stokes system, anisotropic Littlewood-Paley theory, global well-posedness. AB -

We consider the global well-posedness of three dimensional incompressible inhomogeneous Navier-Stokes equation 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 and the initial density is close enough to a positive constant, we prove the global well-posedness of this system. This result extends the previous results in [9, 11] for the classical Navier-Stokes system.

Hao , Tiantian. (2021). Global Solutions of 3-D Inhomogeneous Navier-Stokes System with Large Viscosity in One Variable. Communications in Mathematical Research . 38 (1). 62-80. doi:10.4208/cmr.2021-0040
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