REPRESENTATION OF VISCOUS HEAT-CONDUCTING GAS FLOWS TRIGONOMETRIC SERIES

Abstract

In the paper, in the case of two independent spatial variables, a complete system of equations is considered Navier-Stokes, whose solutions describe the movements of a compressible viscous heat-conducting gas. For it, the Cauchy problem with continuous initial data is posed squared on the xOy plane. After a corresponding continuation of these data on the second square, the solution of the Cauchy problem is presented in the form of corresponding trigonometric series for spatial variables. The coefficients of the series are the desired functions of time. An infinite system of ordinary differential equations with corresponding initial conditions is given for these coefficients. Finite segments of trigonometric sums are constructed, approximating the solutions of the Cauchy problem under consideration.