Spectral analysis of linearized stationary equations of viscous compressible fluid in ℝ³, with periodic boundary conditions

Pribyl′, M.

doi:10.1090/S1061-0022-09-01047-4

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

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