广义流体力学与经典流体力学极限
Generalized hydrodynamics and the classical hydrodynamic limit
摘要：
这项工作是关于我们最近发展的非平衡态热力学的形式主义。这种形式扩展了经典的不可逆热力学，导致经典热力学，不能描述长弛豫的物理现象。利用推广的理论，我们得到了一个广义的流体力学系统，它可以用来描述非牛顿流体，超越傅立叶定律的传热和在很短的时间和空间尺度上的流体流动。我们研究了广义水动力系统的数学结构，证明了它具有良好的守恒-耗散结构，因而是可对称化的双曲型。此外，我们严格证明了当弛豫时间趋于零时，该广义流体力学系统趋于经典流体力学。这表明，经典流体力学可以作为我们的广义流体力学的近似导出。
英文摘要：
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena with long relaxations. With the extended theory, we obtain a generalized hydrodynamic system which can be used to describe the non-Newtonian fluids, heat transfer beyond Fourier's law and fluid flow in very short temporal and spatial scales. We study the mathematical structure of the generalized hydrodynamic system and show that it possesses a nice conservation-dissipation structure and therefore is symmetrizable hyperbolic. Moreover, we rigorously justify that this generalized hydrodynamic system tends to the classical hydrodynamics when the relaxation times approach to zero. This shows that the classical hydrodynamics can be derived as an approximation of our generalized one.
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