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Spectral analysis of linearized stationary equations of viscous compressible fluid in $ \mathbb{R}^3$, with periodic boundary conditions


Author: M. A. Pribyl'
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 20 (2008), nomer 2.
Journal: St. Petersburg Math. J. 20 (2009), 267-288
MSC (2000): Primary 35Q35
DOI: https://doi.org/10.1090/S1061-0022-09-01047-4
Published electronically: February 4, 2009
MathSciNet review: 2423999
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Abstract: The operator whose spectrum is studied corresponds to linearized stationary equations of viscous compressible fluid in $ \mathbb{R}^3$, 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.


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Additional Information

M. A. Pribyl'
Affiliation: Institute for System Studies, Russian Academy of Sciences, Moscow, Russia
Email: marina.pribyl@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-09-01047-4
Keywords: Viscous compressible fluid, linearization, periodic boundary condition
Received by editor(s): May 15, 2007
Published electronically: February 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society