非等熵Navier-Stokes/Allen-Cahn方程组解的性态研究

具有扩散界面的两相流模型可以有效刻画两种流体在流动过程中分界面出现大变形或拓扑形变的流体现象，其数学理论的研究逐步引起了数学界的关注。对这类方程的研究，不仅有重大的理论意义，而且随着问题的解决也必将会对某些物理现象的解释提供重要的参考。本项目拟围绕一维非等熵Navier-Stokes/Allen-Cahn方程组柯西问题由粘性接触间断和两个稀疏波叠加的复合波的非线性稳定性以及三维非等熵Navier-Stokes/Allen-Cahn方程组柯西问题整体解的存在性和大时间行为等方面展开系统深入的研究，期望在这些方面取得突破性的进展。

The two-phase flow model with diffusion interface can effectively describe the phenomenon of large deformation or topological deformation on the interface of two kinds of fluids in the process of flow. Theoretical study of mathematics on non-isentropic Navier-Stokes/Allen-Cahn equations gradually attracted the attention of many mathematicians. The study of this kind of equation, not only is the theoretically significant, but also will provide important reference to explain some physical phenomena. This project is concerned with the nonlinear stability of the composite wave consisting of two rarefactions and a viscous contact discontinuity on one-dimensional non-isentropic Navier-Stokes/Allen-Cahn equations, as well as the asymptotic stability and large-time behavior of solutions to the Cauchy problem on three-dimensional non-isentropic Navier-Stokes/Allen-Cahn equations. We expect a breakthrough in these aspects.