可压缩Navier-Stokes-Vlasov-Fokker-Planck方程及相关模型解的适定性

粒子和可压流体相互作用模型来源于流体力学等应用学科，出现在生物技术和化学工程等应用领域中。数学上，该模型由可压缩Navier-Stokes方程和Vlasov-Fokker-Planck方程耦合而成。因此，对该模型的研究不仅可以建立关于其自身的数学理论，还有可能完善可压缩Navier-Stokes方程以及相关模型的数学理论。目前对该模型的研究还不多，本项目将综合运用能量方法、弱收敛方法以及谱分析方法等研究可压缩Navier-Stokes方程耦合Vlasov-Fokker-Planck方程以及对应宏观模型解的适定性以及流体动力学极限等问题。

Compressible fluid-particle interactions model, arising in fluid dynamics and other related subjects, has applications to biotechnology, chemical engineering and other fields. Mathematically, the model consists of compressible Navier-Stokes equations coupled with Vlasov-Fokker-Planck/equations. Therefore doing research on the model is not only good for establishing its mathematical theory but also for possibly making the mathematical theory for compressible Navier-Stokes equations and related models more complete. There are only a few mathematical results on the model. In this project, we will use energy method, weak compactness arguments and spectrum analysis to study the well-posedness and hydrodynamic limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck equations and its macroscopic model.