相对论流体自由界面问题的适定性及渐近行为

本项目主要研究三类重要的相对论流体力学模型的自由界面问题，包括可压缩相对论Euler方程、可压缩相对论Euler-Poisson方程和可压缩相对论MHD（磁流体）方程等。重点研究：高维可压缩相对论Euler方程与可压缩相对论MHD方程的涡面解及接触间断解的存在性、稳定性以及非相对论极限等问题；高维可压缩相对论Euler方程和可压缩相对论Euler-Poisson方程真空自由边界问题光滑解的适定性以及非相对论极限等问题。本项目研究的内容源于等离子体物理、核物理、天体物理、宇宙学等众多领域，具有鲜明的应用科学背景，是国际上十分重视且具有前沿性的热点研究问题之一，有重要的理论意义。

In this project, we study the free surface problems for three kinds of important relativistic fluids including the compressible relativistic Euler equation, compressible relativistic Euler-Poisson equation and the compressible relativistic MHD equation. We mainly investigate the existence, stability and related non-relativistic limits of vortex sheets and contact discontinuities for both the high dimensional compressible relativistic Euler equation and the relativistic MHD equation，and consider the well-posedness and non-relativistic limits for the smooth solutions to the free boundary value problems of both the compressible relativistic Euler equation and the relativistic Euler-Poisson equation. These issues have a very distinct background of applied science, and are one of hot research issues that are highly valued and frontier in the world.