• 科學研究
    報告題目:

    Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations

    報告人:

    姚磊 教授(西北大學)

    報告時間:

    報告地點:

    理學院東北樓四樓報告廳(404)

    報告摘要:

    We study the hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations in a two or three dimensional bounded domain when the initial density is bounded away from zero. The proof relies on the relative entropy argument to obtain the strong convergence of macroscopic density of the particles $n^{\epsilon}$ in $L^{\infty}(0,T;L^{1}(\Omega))$, which extends the works of Goudon-Jabin-Vasseur [2004,Indiana] and Mellt-Vasseur [2008,CMP] to inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations. Furthermore, when the initial density may vanish, taking advantage of compactness result $L_M\hookrightarrow\hookrightarrow H^{-1}$ of Orlicz spaces in 2D, we obtain the convergence of $n^{\epsilon}$ in $L^{\infty}(0,T;H^{-1}(\Omega))$, which is used to obtain the relative entropy estimate, thus we also show the hydrodynamic limit for 2D inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations when there is initial vacuum.

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