Parabolicity of a Quasihydrodynamic System of Equations and the Stability of its Small Perturbations

We establish that the quasihydrodynamic system of equations of motion of a perfect polytropic gas is parabolic (in the sense of Petrovskii). We study the stability of small perturbations on a constant background and, for the Cauchy problem and the initial boundary-value problems for the corresponding linearized system, we obtain uniform (on the infinite time interval) estimates of relative perturbations. The corresponding results are also derived in the barotropic case for a general equation of state.