具有外力的两相流体模型在周期域上的时间周期解
Time periodic solution to the two-phase fluid model with an external force in a periodic domain
周莹颜 1郭闪闪1
作者信息
- 1. 重庆师范大学数学科学学院,重庆 401331
- 折叠
摘要
考虑两相流体模型的时间周期解问题,该系统由可压缩的等温Euler方程和可压缩的等熵Navier-Stokes方程通过阻力项耦合而成的.该模型最先是从具有强局部对准力的Vlasov-Fokker-Planck/可压缩Navier-Stokes模型中取流体动力学极限推导得出的.基于正则化逼近和拓扑度理论,在小时间周期外力作用下,在周期域中得到了时间周期解的存在性.此外,通过能量估计,证明了时间周期解的唯一性.
Abstract
The time periodic solution to a two-phase fluid system is considered,which is consisted of the compressible i-sothermal Euler equations coupled with the compressible isentropic Navier-Stokes equations through a drag forcing term.This model was first derived by taking the hydrodynamic limit from the Vlasov-Fokker-Planck/isentropic Navier-Stokes equations with strong local alignment forces.Based on regularized approximation and the topological degree theory,we obtain the exist-ence of time periodic solutions under some smallness and structure assumptions imposed on the time periodic force in the peri-odic domain.Moreover,by energy methods,The uniqueness of the time periodic solution is proved.
关键词
时间周期解/Euler方程/Navier-Stokes方程/拓扑度理论/能量估计Key words
time periodic solution/Euler equations/Navier-Stokes equations/topological degree/energy method引用本文复制引用
基金项目
国家自然科学基金(12001074)
重庆市教委科学技术研究计划(KJQN202000536)
重庆市科技局科学研究项目(cstc2020jcyjmsxmX0606)
出版年
2024
NETL
NSTL
万方数据