Some Paradoxes of Mathematical Theory of Continues Mechanics
American Journal of Applied Mathematics
Volume 6, Issue 1, February 2018, Pages: 15-19
Received: Jan. 11, 2018; Accepted: Jan. 29, 2018; Published: Mar. 7, 2018
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Author
Evelina Prozorova, Mathematic and Mechanic Faculty, St. Peterburg State University, Peterhof, Russia
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Abstract
The 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 self-diffusion and thermo-diffusion which were foretold by S. V. Vallander are obtained from kinetic theory.
Keywords
Angular Momentum, Conservation Laws, Non-Symmetrical Stress Tensor, Boltzmann Equations, Chapman-Enskog Method, Conjugate Problem the Navie-Stokes
To cite this article
Evelina Prozorova, Some Paradoxes of Mathematical Theory of Continues Mechanics, American Journal of Applied Mathematics. Vol. 6, No. 1, 2018, pp. 15-19. doi: 10.11648/j.ajam.20180601.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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