论文标题
相对论欧拉方程的全球熵解决方案和牛顿的极限
Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations
论文作者
论文摘要
我们通过一般压力定律分析了巴里昂数量和动量的保护定律的相对论欧拉方程。通过开发一个补偿的紧凑型框架，建立了系统的全球有限熵解决方案的存在。证明依赖于对熵和熵频率函数的仔细分析，这些函数由相对论欧拉方程的熵和熵 - 频率方程的基本解表示。基于仔细的熵分析，我们建立了一个紧凑型框架，用于精确溶液的序列和相对论欧拉方程的近似解决方案。然后，我们通过消失的粘度方法构建近似解决方案，并采用我们的紧凑型框架推断出熵溶液的全球及时存在。还建立了解决方案操作员的紧凑性。最后，我们将技术应用于从相对论欧拉方程的熵解决方案到经典的欧拉方程的熵解决方案的融合。
We analyze the relativistic Euler equations of conservation laws of baryon number and momentum with a general pressure law. The existence of global-in-time bounded entropy solutions for the system is established by developing a compensated compactness framework. The proof relies on a careful analysis of the entropy and entropy-flux functions, which are represented by the fundamental solutions of the entropy and entropy-flux equations for the relativistic Euler equations. Based on the careful entropy analysis, we establish a compactness framework for sequences of both exact solutions and approximate solutions of the relativistic Euler equations. Then we construct approximate solutions via the vanishing viscosity method and employ our compactness framework to deduce the global-in-time existence of entropy solutions. The compactness of the solution operator is also established. Finally, we apply our techniques to establish the convergence of the Newtonian limit from the entropy solutions of the relativistic Euler equations to the classical Euler equations.
