Spectral analysis of linearized stationary equations of viscous compressible fluid in $\mathbb {R}^3$, with periodic boundary conditions
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M. A. Pribyl′
Translated by: A. Plotkin - St. Petersburg Math. J. 20 (2009), 267-288
- DOI: https://doi.org/10.1090/S1061-0022-09-01047-4
- Published electronically: February 4, 2009
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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.References
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Bibliographic Information
- M. A. Pribyl′
- Affiliation: Institute for System Studies, Russian Academy of Sciences, Moscow, Russia
- Email: marina.pribyl@gmail.com
- Received by editor(s): May 15, 2007
- Published electronically: February 4, 2009
- © Copyright 2009 American Mathematical Society
- Journal: St. Petersburg Math. J. 20 (2009), 267-288
- MSC (2000): Primary 35Q35
- DOI: https://doi.org/10.1090/S1061-0022-09-01047-4
- MathSciNet review: 2423999