Abstract
In this article, we study the solutions of the damped Navier–Stokes equation with the Navier slip boundary condition in a bounded domain \(\Omega \) in \({\mathbb {R}}^3\) with sufficiently smooth boundary. We employ the Galerkin method to approximate the solutions of the damped Navier–Stokes equations with the Navier-slip boundary conditions. The existence of the solutions is global for \(\beta \ge 1\). We also established the regularity of the solutions for \(\beta \ge 3\), and the uniqueness of the solutions for \(\beta \ge 1\).
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Acknowledgements
The first author acknowledge the Grant from NBHM (Grant No. 02011/9/2019 NBHM(R.P.)/R and D II/1324) and the second author is supported by the DST MATRICS (Grant No. SERB/F/12082/2018-2019). The authors thank the editor and anonymous reviewers whose valuable and insightful comments have helped to improve the original manuscript.
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Pal, S., Haloi, R. Existence and uniqueness of solutions to the damped Navier–Stokes equations with Navier boundary conditions for three dimensional incompressible fluid. J. Appl. Math. Comput. 66, 307–325 (2021). https://doi.org/10.1007/s12190-020-01437-1
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DOI: https://doi.org/10.1007/s12190-020-01437-1