Geodesic
Spectral analysis of linearized stationary equations of viscous compressible fluid in $\mathbb{R}^3$, with periodic boundary conditions
Algebra i analiz, Tome 20 (2008) no. 2, pp. 149-177 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Viscous compressible fluid
Keywords: linearization, periodic boundary condition. 
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M. A. Pribyl'. Spectral analysis of linearized stationary equations of viscous compressible fluid in $\mathbb{R}^3$, with periodic boundary conditions. Algebra i analiz, Tome 20 (2008) no. 2, pp. 149-177. http://geodesic.mathdoc.fr/item/AA_2008_20_2_a5/

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