In many areas of science and technology, one encounters the necessity to investigate the flow of liquids and gases in, for example, aviation and aeronautics, the car industry, the design of turbines, compressors and pumps, the chemical and food industry, medicine, biology, agriculture, meteorology, hydrology, oceanography and environmental protection. In the preface of the well-known book (Landau and Lifschitz, 1959) by L. D. Landau and E. M. Lifschitz, fluid dynamics is characterized as a branch of theoretical physics. The fundamental concepts and equations of fluid dynamics are connected with the names of Newton, Euler, Cauchy, Lagrange, Bernoulli, Huygens, d'Alembert, Kirchhoff, Helmholtz, Lamb, Stokes, Navier and others and belong to the area of classical rational mechanics. Therefore, it is natural that fluid dynamics uses extensive mathematical tools, particularly partial differential equations, and can also be considered as a mathematical science.

An image of flow can be obtained in two ways:

1. With the aid of experiments, which may give a realistic picture of real flow. In a number of cases the experimental investigation of a flow requires great cost, is lengthy and sometimes impossible, such as in the flow around space vehicles at re-entry or a loss-of-coolant accident in a nuclear reactor.

2. With the use of mathematical models. Most fluid dynamical models are represented by a system of partial differential equations expressing the fundamental laws of conservation of mass, momentum and energy, completed by constitutive relations and thermodynamical laws, together with boundary and initial conditions.

Theoretical investigation of the models...