Representation of the solutions of the Navier-Stokes system near the contact characteristic
It is shown, for the system of Navier-Stokes equations describing the flows of a viscous, heat conducting compressible fluid, that the contact surface is a characteristic of unit multiplicity. The conditions are obtained, which must be specified, for the unique solvability of the corresponding Cauchy problem. It is shown that if the initial data of the problem are analytic, then so is its solutions, and an algorithm is given for constructing it. A transport equation is written out for a weak shock at the contact surface. A solution of the transport equation is given for one-dimensional, plane-symmetric flows, and the form of the first coefficients of the series describing the flow. The time exponent is revealed, which determines the process of smoothing the small perturbations near the corresponding contact surfaces. Solutions decaying with time are constructed in the form of series in powers of this exponent. The first terms of the series are periodic functions of the spatial variable. Two fundamental frequencies can be singled out in the periodic terms, and the frequencies are inversely proportional to the viscosity. The possibility of corresponding oscillations appearing in a flow of viscous gas is discussed.
viscous, heat conducting compressible fluid
scientific article; zbMATH DE number 4087296