0553310 - MÚ 2023 RIV DE eng J - Journal Article
Galdi, G. P. - Neustupa, Jiří
Nonlinear spectral instability of steady-state flow of a viscous liquid past a rotating obstacle.
Mathematische Annalen. Roč. 382, 1-2 (2022), s. 357-382. ISSN 0025-5831. E-ISSN 1432-1807
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equation * nonlinear operator
OECD category: Pure mathematics
Impact factor: 1.4, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s00208-020-02045-x

We show that a steady-state solution to the system of equations of a Navier–Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator L has a part of the spectrum in the half-plane {λ∈C,Reλ>0}. Our result does not follow from known methods, mainly because the basic nonlinear operator is not bounded in the same space in which the instability is studied. As an auxiliary result of independent interest, we also show that the uniform growth bound of the C-semigroup e Lt is equal to the spectral bound of operator L.
Permanent Link: http://hdl.handle.net/11104/0328276