This article is cited in 4 papers

Research Papers

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

M. A. Pribyl'


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.

Keywords: Viscous compressible fluid, linearization, periodic boundary condition.

MSC: 35Q35

Received: 15.05.2007

 English version: St. Petersburg Mathematical Journal, 2009, 20:2, 267–288

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