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

报告人：王腾  教授

报告时间：2018年11月10日（星期六）上午10：30-11：30

报告地点：创新园大厦A1101

校内联系人：王文栋   联系电话：84708351-8139

摘要: 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.

报告人介绍：

王腾，北京工业大学数理学院校聘教授。2015年博士毕业于中国科学院数学与系统科学研究院。主要研究流体力学方程和动力学方程解的极限行为，部分成果发表在数学领域著名杂志Arch. Ration. Mech. Anal., SIAM J. Math. Anal., Indiana Univ. Math. J., Nonlinearity，J. Differential Equations等。目前主持国家自然科学基金一项。