论对流定理证明中的数学缺陷--对连续介质力学及其它经典场论的启示
On Mathematical Defect in Demonstration of Convection Theorem: Implications For Continuum Mechanics and Other Classical Field Theories
摘要：
连续介质力学中的重要运动学定理对流（或输运）定理存在严重的数学缺陷。我们声称，传统的演示没有考虑到一个特殊的约束被积函数给出拉格朗日表示。因此，我们怀疑从某些经典场论的物理定律的积分公式到它们的微分形式的过渡的传统程序在数学上是严格的。重新考虑的公式显示了连续介质力学和其他一些场论的基本微分方程系统如何可以在不改变原始积分公式的情况下进行修改。作为修正的例子，讨论了连续介质的连续性方程和运动方程的微分形式。
英文摘要：
Serious mathematical defect in the important kinematics theorem known in continuum mechanics as Convection (or Transport) Theorem is reported. We claim that the traditional demonstration does not take into account a special constraint on integrand functions given in Lagrangian representation. Thus, we put in doubt that the traditional procedure for the transition from integral formulations of physical laws of some classical field theories to their differential form is mathematically rigorous. Reconsidered formulation shows the way how the system of fundamental differential equations of continuum mechanics and some other field theories could be modified without any change of the original integral formulation. The continuity equation and the differential form of the equation of motion for continuous media are discussed as examples of modification.
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