Justification of Stokes hypothesis and Navier-Stokes first exact transformation for viscous compressible fluid

In this paper Stokes' hypothesis receives the physical justification and alternative mathematical formulation. An alternative formulation is more general and easily checked. As well as in linear elasticity, the pressure in Navier-Stokes equations can be eliminated as unknown function. To do this transformation it is necessary to use the well known derivation analogies of Navier-Cauchy (also called Lame's) equations. In this case the well known problem of “second viscosity” disappears. Thus the fundamental defining relation for pressure is no longer necessary and the Navier-Stokes and Lame's equations exactly coincide. The Navier-Stokes equations are not physically exact because the traditional assumption of const bulk viscosity is not correct. The analysis presented here corrects this error and more exact Navier-Stokes equations have been proposed. This paper written in a way that gives insight to mathematicians, physicists, engineers and students who may not be experts in this topic.