The steady Navier–Stokes problem with the inhomogeneous
Navier-type boundary conditions in a 2D multiply-connected bounded domain

Jiří Neustupa

doi:10.1515/anly-2014-1304

Published by Oldenbourg Wissenschaftsverlag June 12, 2015

The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain

Jiří Neustupa

From the journal Analysis

https://doi.org/10.1515/anly-2014-1304

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Abstract

We assume that Ω is a bounded domain in ℝ2 with N holes. We study the steady Navier–Stokes problem with inhomogeneous Navier-type boundary conditions in Ω (problem BVP-1) and the two other related problems BVP-2 and BVP-3. We prove the existence of strong solutions of BVP-2 and BVP-3 and the uniqueness of solutions for “small data”. The existence of a strong solution of BVP-1 is proven only if the body force 𝐟 belongs to a certain set 𝔐(ℝN). We show that problem BVP-1 is not solvable for some configurations of given boundary data and body forces.