SPECTRAL ANALYSIS OF LINEARIZED STATIONARY EQUATIONS OF VISCOUS COMPRESSIBLE FLUID IN R3, WITH PERIODIC BOUNDARY CONDITIONS

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