Abstract:
The operator whose spectrum is studied corresponds to linearized stationary equations of viscous compressible fluid in R3, with periodic boundary conditions. The equations are obtained by linearization of the nonlinear model equations of viscous compressible fluid near an arbitrary solution depending on the variable x. It is proved that the operator in question is sectorial and that its spectrum is discrete. Also, a subset of the complex plane that contains the spectrum is described. The resolvent is estimated off a sector in the complex plane that is symmetric with respect to the real axis.
Citation:
M. A. Pribyl', “Spectral analysis of linearized stationary equations of viscous compressible fluid in R3, with periodic boundary conditions”, Algebra i Analiz, 20:2 (2008), 149–177; St. Petersburg Math. J., 20:2 (2009), 267–288
\Bibitem{Pri08}
\by M.~A.~Pribyl'
\paper Spectral analysis of linearized stationary equations of viscous compressible fluid in~$\mathbb{R}^3$, with periodic boundary conditions
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 2
\pages 149--177
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\zmath{https://zbmath.org/?q=an:1206.35209}
\elib{https://elibrary.ru/item.asp?id=11568872}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 2
\pages 267--288
\crossref{https://doi.org/10.1090/S1061-0022-09-01047-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267497500006}
Linking options:
https://www.mathnet.ru/eng/aa537
https://www.mathnet.ru/eng/aa/v20/i2/p149
This publication is cited in the following 4 articles:
Gusev N.A., “Asymptotic properties of linearized equations of low compressible fluid motion”, J. Math. Fluid Mech., 14:3 (2012), 591–618
N. A. Gusev, “Slabaya i silnaya skhodimost reshenii linearizovannykh uravnenii slaboszhimaemoi zhidkosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 47–52
Pribyl M., “Analysis of spectral properties of operators for linearized steady-state equations of a viscous compressible heat-conducting fluid”, J. Dyn. Control Syst., 17:2 (2011), 187–205
M. A. Pribyl, “Spectral analysis of linearized stationary equations of a compressible viscous fluid”, Sb. Math., 198:10 (2007), 1495–1515
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