当流体中含有分散的悬浮颗粒时，流体和粒子之间会相互影响。可以用流体—动力学耦合方程组刻画它们的运动规律。该模型广泛应用于气溶胶、喷雾器、污水循环、柴油发动机和火箭助推器等领域。据申请人所知，目前，关于流体—动力学耦合方程组已有的数学结论，大多涉及一般弱解的整体存在性，或在常数平衡态附近小初值光滑解的整体（局部）适定性，以及解的时间衰减速率。基本波（激波、疏散波和接触间断波）现象是双曲守恒律方程组的重要特征，已经有了较丰富的研究成果。但是，关于流体—动力学耦合模型基本波现象的研究目前还没有任何进展。.申请人一直从事动力学方程和流体力学方程基本波的研究，取得了一些初步进展。本项目拟对一类流体—动力学耦合方程组的基本波现象进行探索研究，即分别证明可压缩Navier-Stokes/Euler-Vlasov-Fokker-Planck方程平面疏散波、粘性接触间断波以及行波解的存在性和稳定性。

The fluid-kinetic system can be described the evolution of dispersed particles in a fluid, in which, the fluid-particles interactions are taken into account. This model is widely used in aerosols, sprays, waste-water recycling and Diesel engines or rocket propulsors. To the best of our knowledge, all results on such fluid-kinetic model in mathematics are for the well-posedness of the general global weak solutions or the small classical solution and the time-decay estimates around the constant equilibrium states. Basic wave patterns are typical feature of the hyperbolic conservation laws, and fruitful research achievements have been completed in the development of this theory. However, there is no any process along this direction of such kind of fluid-kinetic type model..Applicant has been involved with studying on wave phenomena of both kinetic equation and hydrodynamic equations, and some investigations have been achieved. This project is devoted to make an exploratory research on the wave phenomena of kinetic equation coupled with fluid mechanics equations, i.e., we plan to investigate the existence and stability of planar rarefaction wave, viscous contact wave and travelling wave for the compressible Navier-Stokes/Euler-Vlasov-Fokker-Planck equations, respectively.