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Global weak solutions for a Vlasov–Fokker–Planck/Navier–Stokes system with nonhomogeneous boundary data

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Abstract

In this paper, we consider a kinetic-fluid model with nonhomogeneous Dirichlet boundary data in a 3D bounded domain. This model consists of a Vlasov–Fokker–Planck equation coupled with the compressible Navier–Stokes equations via a friction force. We establish the global existence of weak solutions to it for the isentropic fluid (adiabatic coefficient \(\gamma > \frac{3}{2}\)) with large initial data, and large velocity and density at the inflow boundary.

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Acknowledgements

The author is very grateful to the nice reviewer for his/her constructive comments and helpful suggestions. She would like to thank Professor Fucai Li and Professor Jinhuan Wang for their fruitful discussions and encouragement during the preparation of this paper. This work is supported by NSFC (Grant Nos. 12071212, 11971234).

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  1. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Yue Li

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Correspondence to Yue Li.

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Li, Y. Global weak solutions for a Vlasov–Fokker–Planck/Navier–Stokes system with nonhomogeneous boundary data. Z. Angew. Math. Phys. 72, 51 (2021). https://doi.org/10.1007/s00033-021-01488-9

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  • DOI: https://doi.org/10.1007/s00033-021-01488-9

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