Unsteady perturbed flow at low Mach number of a viscous compressible fluid

The problem of the unsteady perturbed two-dimensional flow at low Mach number of a viscous compressible fluid is studied taking the relation between the stress and deformation rates tensors that was obtained and applied in [1] and [3]. It is shown that the system of equations describing the phenomenon is totally hyperbolic and therefore the perturbations in any point $P$ of the field are propagated by means of waves corresponding to four characteristic surfaces passing through $P$. The displacement and propagation velocities of these waves are determined as well as their dependence on the orientation of their front in $P$; it is shown besides that the discontinuity vector across the waves has components both longitudinal and transversal. The variation laws of the fluid velocities both on the characteristic surfaces and along their bicharacteristics are determined, which allows us to solve the Cauchy problem with a “step-by-step” method.