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

  • Jiří Neustupa EMAIL logo
Published/Copyright: June 12, 2015
Analysis
From the journal Analysis Volume 35 Issue 3

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.

Keywords: Steady Navier–Stokes problem; slip boundary conditions
MSC: 35Q30; 35J65; 76D03; 76D05

Funding source: Grant Agency of the Czech Republic

Award Identifier / Grant number: 13-00522S

Funding source: Academy of Sciences of the Czech Republic

Award Identifier / Grant number: RVO 67985840

Received: 2014-12-8
Revised: 2015-3-26
Accepted: 2015-4-30
Published Online: 2015-6-12
Published in Print: 2015-8-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
  3. Strong solutions of the Boussinesq system in exterior domains
  4. Some stability results on global solutions to the Navier–Stokes equations
  5. The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
  6. Global regularity for a model Navier–Stokes equations on ℝ3
  7. The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
https://doi.org/10.1515/anly-2014-1304
Keywords for this article
Steady Navier–Stokes problem; slip boundary conditions

Articles in the same Issue

  1. Frontmatter
  2. Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
  3. Strong solutions of the Boussinesq system in exterior domains
  4. Some stability results on global solutions to the Navier–Stokes equations
  5. The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
  6. Global regularity for a model Navier–Stokes equations on ℝ3
  7. The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
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