A spectral criterion for stability of a steady viscous incompressible flow past an obstacle

0457135 - MÚ 2017 RIV CH eng J - Journal Article
Neustupa, Jiří
A spectral criterion for stability of a steady viscous incompressible flow past an obstacle.
Journal of Mathematical Fluid Mechanics. Roč. 18, č. 1 (2016), s. 133-156. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * Oseen equation * stability
Subject RIV: BA - General Mathematics
Impact factor: 1.106, year: 2016
http://link.springer.com/article/10.1007/s00021-015-0239-0

We show that the question of stability of a steady incompressible Navier-Stokes flow V in a 3D exterior domain Ω is essentially a finite-dimensional problem (Theorem 3.2). Although the associated linearized operator has an essential spectrum touching the imaginary axis, we show that certain assumptions on the eigenvalues of this operator guarantee the stability of flow V (Theorem 4.1). No assumption on the smallness of the steady flow V is required.
Permanent Link: http://hdl.handle.net/11104/0257549