Group Classification of the Navier-Stokes Equations for Compressible Viscous Heat-Conducting Gas

We consider the problems of using computer algebra systems for group classification of partial differential equations. The presence of arbitrary elements makes the solution of determining equations more difficult. It offers necessity for active human control over this process by using dialog regime. Methods of computer algebra for problems of group classification are illustrated by the example of a system of the Navier-Stokes equations for compressible viscous heat-conducting gas. This system has five arbitrary elements. The solution of the problem of finding equivalence transfonpations is presented. The group classification is carried out in some particular cases.