Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

Quanrong Li; Shijin Ding

doi:10.3934/cpaa.2021121

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2021, Volume 20, Issue 10: 3561-3581. Doi: 10.3934/cpaa.2021121 open access

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Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

Quanrong Li^1, and
Shijin Ding^2, ,

1.
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, Guangdong, China
2.
South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, 510631, Guangdong, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2019

Revised: May 31, 2021

Early access: July 2021

Published: October 2021

Li's research is supported by the National Natural Science Foundation of China(No.11901399) and the Natural Science Foundation of Shenzhen University (2019084). Ding's research is supported by the National Natural Science Foundation of China (No.11371152, No.11571117, No.11871005 and No.11771155), Natural Science Foundation of Guandong Province (No.2017A030313003 and No.2021A1515010303) and Science and Technology Program of Guangzhou (No.2019050001)

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Abstract

This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have defined sign. In the meantime, we also establish a number of Gagliardo-Nirenberg inequalities in the corresponding Sobolev spaces which will be applicable to other similar situations.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76N10.

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