可压相对论Euler方程及相关模型的适定性研究

本项目拟研究可压相对论Euler方程及相关模型自由边界问题、Cauchy问题和初边值问题光滑解的适定性和渐近极限等问题。一方面研究可压相对论Euler方程、可压相对论Euler-Poisson方程及相关模型自由边界问题局部和整体光滑解适定性、大时间渐近状态、非相对论极限和松弛极限等问题；另一方面本项目研究相对论Euler-Poisson方程及相关模型大初值Cauchy问题和初边值问题平衡态光滑解的适定性、光滑解的适定性及大时间渐近状态、以及相关的非相对论极限和松弛极限等问题。 本项目研究的问题具有很强的应用科学背景，是非线性科学研究的重点之一，有重要的理论意义。

In this project, we study the well-posedness and asymptotic limits of smooth solutions for the free boundary value problem, Cauchy problem and initial boundary value problem of the relativistic Euler equation and related models. On the one hand, we consider the well-posedness, large time behaviors, non-relativistic limits and relaxation limits of local and global smooth solutions to the relativistic Euler, the relativistic Euler-Poisson and related models; On the other hand, we consider the well-posedess of smooth steady state solutions, the well-poseness and the large time behaviors of smooth solutions , the related non-relativistic limits and relaxation limits of the Cauchy problem and the initial boundary value problem with large initial data to the relativistic Euler-Poisson equation and related models.