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Journal of Applied Mathematics and Computing

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26-09-2020 | Original Research

Existence and uniqueness of solutions to the damped Navier–Stokes equations with Navier boundary conditions for three dimensional incompressible fluid

Authors: Subha Pal, Rajib Haloi

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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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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Title: Existence and uniqueness of solutions to the damped Navier–Stokes equations with Navier boundary conditions for three dimensional incompressible fluid
Authors: Subha Pal
Rajib Haloi
Publication date: 26-09-2020
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01437-1

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