论文标题
非等渗多潮流气流的补偿紧凑方法
Compensated Compactness Method on Non-isentropic Polytropic Gas Flow
论文作者
论文摘要
在本文中，我们关注的是多变态气流的模型，该模型包括质量方程，动量方程和不同的熵方程。首先，是一种新技术，以建立等肌系统的Riemann不变性与熵变量$ s $之间的关系，并加上最大原则，以获取粘度 - 即近似近似解决方案的Apriori $ l^{\ infty} $估计。其次，采用了层状气体动力学系统的补偿紧凑性理论的收敛框架，以证明近似解决方案的偶然收敛性，以及具有有界初始数据的系统的凯奇问题的有界熵解决方案的全球存在。最后，作为一种副产品，我们获得了原始非凝集的多流气气流的非经典有限的广义解$（ρ，u，s），$，它满足质量方程和动量方程，熵方程在分布方面具有额外的非负量度。
In this paper, we are concerned with a model of polytropic gas flow, which consists the mass equation, the momentum equation and a varying entropy equation. First, a new technique, to set up a relation between the Riemann invariants of the isentropic system and the entropy variable $s$, coupled with the maximum principle, is introduced to obtain the a-priori $L^{\infty}$ estimates for the viscosity-flux approximation solutions. Second, the convergence framework from the compensated compactness theory on the system of isentropic gas dynamics is applied to prove the pointwise convergence of the approximation solutions and the global existence of bounded entropy solutions for the Cauchy problem of the system with bounded initial data. Finally, as a by-product, we obtain a non-classical bounded generalized solution $(ρ,u,s),$ of the original non-isentropic polytropic gas flow, which satisfies the mass equation and the momentum equation, the entropy equation with an extra nonnegative measure in the sense of distributions.
