Analysis of spectral properties of operators for linearized steady-state equations of a viscous compressible heat-conducting fluid

The spectrum of operators for linearized steady-state equations of a viscous, compressible, heat-conducting fluid is studied. Using the factorization of operators and applying the theory of pseudo-differential operators, we prove that the operator is sectorial and its spectrum is discrete everywhere except for some segment on the real line. This segment is the essential spectrum of the operator and it lies in the left half-plane.