The Navier-Stokes equations describe the motion of the usual fluids like water, air, oil under quite general conditions. They are the base of the mathematical models of important phenomena in many areas of science and technology. While the physical model leading to the Navier-Stokes is simple their understanding, from mathematical point of view, remains fundamentally incomplete. Anyway the study of this equations has stipulated and influenced treatment, improved and refined the methods of research in partial differential equations. Rightly, they are one of the most celebrate system of equations of Applied Mathematics. Recently, due to the progress in Marthematical Analysis and Computer Science the research on Navier-Stokes benefited of a rivitalizing attention. The last years have brought bulk of achievements survey articles, books and an increasing number of research papers. Further, numerical and computational methods become another focus for the applications of the basic theory. The Navier-Stokes equations are studied in all parts of the world and in all areas of research that are intimately connected with the basic mathematical theory of the equations. It is clear that the attempt to understand the equations and in general the nonlinear problems will dominate large parts of mathematics in most areas of science and technology in the future years. The topics of the Conference move around actual research on the qualitative theory, the progress performed in the flow with free surface and the relevant results on the theory of compressible fluids. A significant part is played by the numerical methods and industrial applications.
The purpose of the Conferences in Varenna, initiated in 1992, are the following: - to promote, encourage, and influence more cooperation in the world community of the researchers on the Navier-Stokes and related problems; - to focus the most actual topics and significant results; - to include pratising professional in academia, industry and government, post doctoral research scolars; - to organize the Conference on the Navier-Stokes equations every three years; - to publish the Conference proceedings.