Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics
Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics
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发表时间：
1981
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通讯作者：
T. Ruggeri;A. Strumia
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作者：
T. Ruggeri;A. Strumia
总结。-考虑守恒形式的一阶拟线性双曲组，作为场方程解的结果，假定存在一个补充守恒律。从K.O.Friedrichs[1]的一篇文章出发，引入了凸协变密度的定义，并通过显式协变形式证明了：a)只依赖于场方程组和补充守恒律，但通过场变量映射不变的“主场？U”存在；b)如果取U‘作为场变量，且对称系统是由一个四元向量生成的，则系统呈对称守恒形式；c)可以在激波流形上定义一个协变标量函数，它提供“熵增长”(在P.D.Lax意义下)；D)前面的函数“生成”激波和激波流形不是类空间的，如果特征流形不是类空间的。最后，证明了相对论流体力学系统具有凸协变密度，并详细讨论了结果的序列a)-d)。
SUMMARY. - A quasi-linear hyperbolic system of the first order, in conservative form, is considered and a supplementary conservation law is supposed to exist, as a consequence of the field equations. Starting from a paper of K. O. Friedrichs [1 ], the definition of convex covariant density is introduced and it is proven through an explicitely covariant formalism that : a) a « main field » U’ exists depending only on the field equations and the supplementary conservation law, but invariant through field variable mapping; b) the system assumes a symmetric conservative form if U’ is chosen as field variable and the symmetric system is « generated » by the knowledge of only one four-vector; c) it is possible to define a covariant scalar function on a shock manifold which provides « entropy growth » (in the sense of P. D. Lax); d) the previous function « generates » the shock and the shock manifold are not space-like if the characteristic ones are not space-like. Finally the system of relativistic fluid dynamics is shown to possess a convex covariant density and conse-quences of the results a)-d) are discussed in detail.