Inviscid Limit of 3D Nonhomogeneous Navier–Stokes Equations with Slip Boundary Conditions

Hongmin Li, Yuanxian Hui () and Zhong Zhao
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Hongmin Li: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Yuanxian Hui: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Zhong Zhao: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Mathematics, 2022, vol. 10, issue 21, 1-12

Abstract: In this paper, we consider the inviscid limit of a nonhomogeneous incompressible Navier–Stokes system with a slip-without-friction boundary condition. We study the convergence in strong norms for a solution and obtain the convergence rate in space W 2 , p ( Ω ) when the boundary is flat. We need to establish the uniform bound of the solution in space W 3 , p ( Ω ) , and the key of proofs is to obtain a priori estimation of ∂ t u in space W 1 , p ( Ω ) .

Keywords: Navier–Stokes equations; nonhomogeneous fluid; slip boundary conditions; inviscid limit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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