标题： 相对论热力学的常规导电流体模型 显示英文标题

标题： The regular conducting fluid model for relativistic thermodynamics

摘要： 这里的“常规”模型可以被认为是构建经典傅里叶-欧拉热传导流体模型的最自然的解决方案，这些模型由两个依赖变量（平衡密度和导电标量）的状态方程所表征。由于埃克特提出的历史上已确立但因果上不令人满意的解决方案被证明是基于一个可解释为在粒子和熵速度及其相关动量之间假定最不自然关系的假设，这解释了该模型众所周知的不良行为，最近已被证明具有非常病态的混合椭圆双曲行为。兰道和利夫希茨的较新（更优雅）解决方案具有更数学上值得尊敬的抛物双曲行为，但仍然仅在诸如静态背景的线性扰动等限制情况下与良好设定的初值问题相容。为了在更一般的条件下具有数学上可接受的行为，并且更不用说满足亚光速信号传播的物理动机要求，只有严格双曲行为是可接受的。这里指出一种更现代的“常规”解决方案的可用性，该方案在所有这些要求方面都完全令人满意。这种“常规”类别的相对论性导电流体模型自然出现在一种最近发展的变分方法中，在这种方法中，传统上重要的应力-动量-能量密度张量被置于次要位置，而相关的协变4动量余向量则被突出显示。 显示英文摘要

摘要： The "regular" model presented here can be considered to be the most natural solution to the problem of constructing the simplest possible relativistic analogue of the category of classical Fourier--Euler thermally conducting fluid models as characterised by a pair of equations of state for just two dependent variables (an equilibrium density and a conducting scalar). The historically established but causally unsatisfactory solution to this problem due to Eckart is shown to be based on an ansatz that is interpretable as postulating a most unnatural relation between the (particle and entropy) velocities and their associated momenta, which accounts for the well known bad behaviour of that model which has recently been shown to have very pathological mixed-elliptic-hyperbolic comportments. The newer (and more elegant) solution of Landau and Lifshitz has a more mathematically respectable parabolic-hyperbolic comportment, but is still compatible with a well posed initial value problem only in such a restricted limit-case such as that of linearised perturbations of a static background. For mathematically acceptable behaviour undermore general circumstances, and a fortiori for the physically motivated requirement of subluminal signal propagation, only strictly hyperbolic behaviour is acceptable. Attention is drawn here to the availability of a more modern "regular" solution which, is fully satisfactory as far as all these requirements are concerned. This "regular" category of relativistic conducting fluid models arises naturally within a recently developed variational approach, in which the traditionally important stress--momentum-energy density tensor is relegated to a secondary role, while the relevant covariant 4-momentum co-vectors are instead brought to the fore.