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Global weak solutions for a kinetic-fluid model with local alignment force in a bounded domain

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This work is supported by NSFC (Grant Nos. 12071212, 11971234) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
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  • We study a kinetic-fluid model in a $ 3D $ bounded domain. More precisely, this model is a coupling of the Vlasov-Fokker-Planck equation with the local alignment force and the compressible Navier-Stokes equations with nonhomogeneous Dirichlet boundary condition. We prove the global existence of weak solutions to it for the isentropic fluid (adiabatic coefficient $ \gamma> 3/2 $) and hence extend the existence result of Choi and Jung [Asymptotic analysis for a Vlasov-Fokker-Planck/Navier-Stokes system in a bounded domain, arXiv: 1912.13134v2], where the velocity of the fluid is supplemented with homogeneous Dirichlet boundary condition.

    Mathematics Subject Classification: Primary: 35Q35, 82C22; Secondary: 35D05, 76N10.


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