MAJESTIBET OFFICIAL SOME PARADOXES OF MATHEMATICAL THEORY OF CONTINUES MECHANICS, AMERICAN JOURNAL OF APPLIED MATHEMATICS, SCIENCE PUBLISHING GROUP

MAJESTIBET classic theory of continuum mechanics does not preserve the continuity of the environment due to the use of the conditions of equilibrium of forces and the symmetry of the stress tensor. We used many unreasonable mathematical approximations when by the Boltzmann equation is solved to describe the equations of continuum mechanics. The paper presents an analysis of mathematical approximations underlying description in different environments, and new models, to avoid the resulting misunderstandings. For rarefied gas the selfdiffusion and thermodiffusion which were foretold by S. V. Vallander are obtained from kinetic theory.