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

0446811 - MÚ 2016 RIV DE eng J - Journal Article
Neustupa, Jiří
The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain.
Analysis. International mathematical journal of analysis and its applications. Roč. 35, č. 3 (2015), s. 201-212. ISSN 0174-4747
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : steady Navier-Stokes problem * slip boundary conditions
Subject RIV: BA - General Mathematics
http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1304/anly-2014-1304.xml

We assume that Ω is a bounded domain in R 2 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(R N ) . We show that problem BVP-1 is not solvable for some configurations of given boundary data and body forces.
Permanent Link: http://hdl.handle.net/11104/0248794