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Stability of planar rarefaction wave to 3D Navier-Stokes/Euler-Vlasov-Fokker-Planck equations


Academic Report

Title: Stability of planar rarefaction wave to 3D Navier-Stokes/Euler-Vlasov-Fokker-Planck equations

Reporter: Prof. WANG Teng (Beijing University of Technology)

Time: November 10, 2018 (Saturday) AM 10:30-11:30

Location: A1101# room, Innovation Park Building

Contact: WANG Wendong (tel:84708351-8139)


Abstract: In this paper, we investigate the wave phenomena to a fluid-particle model described by the three-dimensional Vlasov-Fokker-Planck equations coupled with the compressible Navier-Stokes/Euler equations (denoted by NS/E-VFP in abbreviation). First, we show that the planar rarefaction wave is time-asymptotic stable for both NS-VFP and E-VFP systems in three dimensions. Furthermore, it can be derived that there exists a smooth solution for NS-VFP system tends to a smooth solution for E-VFP system with some convergence rate as viscosity coefficients tend to zero, in which both the smooth solutions are around the smooth rarefaction wave. It should be noted that such a wave phenomena has never been observed from the pure Fokker-Planck equation and compressible fluids with damping term,which comes essentially from the relaxation interactions between fluid part (the compressible Navier-Stokes/Euler equations) and the kinetic part (Vlasov-Fokker-Planck equations) through the friction force.


The brief introduction to the reporter: Wang Teng, Professor of mathematics and physics, Beijing University of Technology. He graduated from the Institute of mathematics and systems science, Chinese Academy of Sciences in 2015. His main research fields are the limit behavior of solutions to hydrodynamic and dynamic equations. Some of his achievements are published in the famous journals, such as Arch. Ration. Mech. Anal., SIAM J. Math. Anal., Indiana Univ. Math. J., Nonlinearity, J. Differential Equations, etc. And he presides over a project of the National Natural Science Foundation of China.