Global Weak Solutions to Compressible Navier–Stokes–Vlasov–Boltzmann Systems for Spray Dynamics
Global Weak Solutions to Compressible Navier–Stokes–Vlasov–Boltzmann Systems for Spray Dynamics
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DOI：
10.1007/s00021-020-00505-7
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发表时间：
2018-06
影响因子：
1.3
通讯作者：
I. Gamba;Cheng Yu
中科院分区：
文献类型：
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作者：
I. Gamba;Cheng Yu
本工作的重点是建立一个模拟可压缩流体中颗粒液滴演化的偏微分积分方程的动力学-流体系统的弱解。该系统由用于宏观描述气体流体流动的标准等熵可压缩Navier-Stokes方程和用于控制以变半径粒子为模型的喷雾液滴演化的Vlasov-Boltzmann型方程耦合给出。建立了具有有限能量的整体弱解的存在性，其气体密度满足重正化质量方程。该证明结合了Feireisl等人（J Math Fluid Mech 3:358-392, 2001）对耦合系统中可压缩Navier-Stokes方程的弱解的启发，通过扩展Leger和Vasseur （J双曲微分方程6(1):185 - 206,2009）为不可压缩流体-动力学系统开发的技术来解决喷雾液滴的动力学问题。
This work focus on the construction of weak solutions to a kinetic-fluid system of partial differential–integral equations modeling the evolution of particles droplets in a compressible fluid. The system is given by a coupling between the standard isentropic compressible Navier–Stokes equations for the macroscopic description of a gas fluid flow, and a Vlasov–Boltzmann type equation governing the evolution of spray droplets modeled as particles with varying radius. We establish the existence of global weak solutions with finite energy, whose density of gas satisfies the renormalized mass equation. The proof combines techniques inspired by the work of Feireisl et al. (J Math Fluid Mech 3:358–392, 2001) on the weak solutions of the compressible Navier–Stokes equations in a coupled system to the kinetic problem for the spray droplets by extending techniques of Leger and Vasseur (J Hyperbolic Differ Equ 6(1):185–206, 2009) developed for the incompressible fluid-kinetic system.