Time periodic solution to the two-phase fluid model with an external force in a periodic domain
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.
time periodic solutionEuler equationsNavier-Stokes equationstopological degreeenergy method
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