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Some Paradoxes of Mathematical Theory of Continues Mechanics

机译:连续力学数学理论的一些悖论

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摘要

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.
机译:由于使用了力的平衡条件和应力张量的对称性,经典的连续介质力学理论不能保持环境的连续性。当通过玻尔兹曼方程求解来描述连续体力学方程时,我们使用了许多不合理的数学近似。本文对在不同环境下进行描述的数学近似方法和新模型进行了分析,以避免产生误解。对于稀薄气体,S。V. Vallander预测的自扩散和热扩散是从动力学理论获得的。

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