一类刻画喷雾模型两相流系统解的存在唯一性  

Existence and Uniqueness of Solution for a Two-phase Flow System Describing Spray Model

作　　者：陈昌飞 蒋鹏 CHEN Changfei;JIANG Peng(College of Science,Hohai University,Jiangsu Nanjing 210098,China)

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《河北师范大学学报（自然科学版）》2021年第1期1-7,共7页Journal of Hebei Normal University：Natural Science

基　　金：江苏省自然科学基金(BK20191296);中央高校业务费(2019B19114)。

摘　　要：讨论了由可压缩Navier-Stokes方程组与Vlasov方程耦合的一类薄的喷雾模型初边值问题光滑解的整体存在性.该模型刻画了在气体和其中悬浮的颗粒物(气溶胶)所组成的两相流系统中,空气与颗粒物自身的运动规律以及两者之间的相互作用.其中颗粒群中的颗粒运动是由气体动力以及颗粒之间相互碰撞的2种力所支配,该运动通过Vlasov方程来刻画,气体的运动则由可压缩Navier-Stokes方程组刻画.利用经典的能量估计方法&并结合颗粒运动的反射边界条件,求出该系统整体光滑解的存在唯一性.This paper mainly discusses the global existence of the smooth solution to the initial boundary value problem for a thin spray model coupled by the compressible Navier-Stokes equations and the Vlasov equation.The model describes the motion law and interaction between air and particulate matter in a two-phase flow system composed of gases and aerosols.The particle movement in the particle group is dominated by the force of gas and the force of collision between particles,which is described by the Vlasov equation,while the gas movement is described by the compressible Navier-Stokes equations.With the classical energy estimation method and the reflection boundary condition of the particle motion,the existence and uniqueness of the global smooth solution to the system is obtained.

关 键 词：喷雾 可压缩Navier-Stokes方程组 Vlasov方程 初边值问题 整体光滑解 

分 类 号：O175.2[理学—基础数学]