无黏流体自由边界问题是流体力学研究中的重要问题，在物理和数学上均有重要意义。本项目拟研究如下几个方面的问题：理想不可压磁流体和弹性流体的自由边值问题；理想可压磁流体和弹性流体的自由边界问题；流体自由边界问题的小参数极限，包括不可压缩极限，零表面张力极限，无黏极限；复杂区域上的流体自由边界问题。这些研究有助于人们更深入地理解磁流体动力学、弹力流体动力学和流体自由边界问题。

Free boundary problems in idea fluids are important to study the fluid dynamics, and are of great interest in both physics and mathematics. In this project, we will study the following problems: free boundary problems in ideal incompressible magnetohydrodynamics and elastodynamics; free boundary problems in ideal compressible magnetohydrodynamics and elastodynamics; small parameter limits in fluid free boundary problems, including incompressible limits, zero surface tension limits and vanishing viscosity limits; fluid free boundary problems with complex geometry. These research will help us to understand magnetohydrodynamics, elastodynamics and free boundary problems more deeply.