王者体育

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科学研究
报告题目:

hydrodynamic limit for the inhomogeneous incompressible navier-stokes/vlasov-fokker-planck equations

报告人:

yaolei jiaoshou(xibeidaxue)

报告时间:

报告地点:

王者体育lixueyuandongbeilousiloubaogaoting(404)

报告摘要:

王者体育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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