ABSTRACT

An important aspect of mathematical physics is the solution of linear nonhomogeneous ordinary differential equations. This chapter provides examples from symbolic dynamics, chaotic dynamical systems, attracting sets and attractors, random fractals and some physical applications including Navier–Stokes equations. It explores three-dimensional Navier–Stokes equations for multicomponent chemical nonequilibrium gas mixtures. For a correct statement of the problem it is necessary to add to Navier–Stokes equations the boundary conditions. For external steady gas dynamic problems the boundary conditions should be given at the body surface and on the infinity. The chapter aims to justify the governing equations for 3d multicomponent nonequilibrium gas flow in the framework of a curvilinear coordinate system. Justification of energy equation is based on two fundamental laws of thermodynamics; they are called the first and the second thermodynamics laws. These laws deal with the concept of internal state and of variables of state.