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

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    * Corresponding author
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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  • 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.

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


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