Spectral analysis of linearized stationary equations of viscous compressible fluid in , 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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The operator whose spectrum is studied corresponds to linearized stationary equations of viscous compressible fluid in , 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 . 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