Model of the Oldroyd compressible fluid

In this paper, mathematical models of compressible viscoelastic Maxwell, Oldroyd, and Kelvin–Voigt fluids are derived. A model of rotating viscoelastic barotropic Oldroyd fluid is studied. A theorem on strong unique solvability of the corresponding initial-boundary value problem is proved. The spectral problem associated with such a system is studied. Results on the spectrum localization, essential and discrete spectra, and spectrum asymptotics are obtained. In the case where the system is in the weightlessness state and does not rotate, results on multiple completeness and basisness of a special system of elements are proved. In such a case, under condition of sufficiently large viscosity, expansion of the solution of the evolution problem with respect to a special system of elements is obtained.