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

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.

The time periodic solution to a two-phase fluid system is considered,which is consisted of the compressible isothermal 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 existence of time periodic solutions under some smallness and structure assumptions imposed on the time periodic force in the periodic domain.Moreover,by energy methods,The uniqueness of the time periodic solution is proved.