粘性激波的非线性稳定性一直都是可压缩流体动力学方程组的重点和难点问题之一。对于这一问题，目前大部分的数学结果都是在激波强度充分小的条件下建立的。因此，大强度激波的稳定性也越来越受到数学家们的关心。本项目将以两类典型的可压缩流体方程组为例来研究大强度激波的稳定性：(1)可压缩Navier-Stokes-Poisson方程组大强度激波的稳定性；(2)可压缩van der Waals方程组大强度激波的稳定性。本项目所研究内容均来源于实际的物理问题，在数学上也具有重要的理论意义。

The nonlinear stability of viscous shock waves has been one of the key and difficult problems of compressible fluid dynamics equations since 19th century. The most of the current mathematical works are established under the condition that the strength of shock wave is small enough. Therefore, more and more mathematicians are concerned with the stability of strong shock waves. In this project, two typical compressible fluid equations are taken as examples to study the stability of large shock waves: (1) The nonlinear stability of large amplitude shock wave to the compressible Navier-Stokes-Poisson equations; (2) The nonlinear stability of large amplitude shock waves of compressible van der Waals equations. The problems come from practical problems with profound physical background and have important theoretical significance in mathematics.