勷勤数学•领军学者报告

题      目：Quasi-neutral limit and the mixer layer problem of Planck-Nernst-Poisson-Navier-Stokes equations for electro-hydrodynamics

报  告  人： 王术 教授  (邀请人：喻洪俊)

                                              北京工业大学

时      间： 9月23日  10：00-11:00

地     点：数科院东楼401

报告人简介:

         王术，现为北京工业大学二级教授、博士生导师、数学博士点责任教授、数学统计学与力学学院学术委员会主任。1998年南京大学博士毕业，后在中国科学院数学所和奥地利维也纳大学做博士后。主要研究方向：偏微分方程及其应用。曾主持国家自然科学基金重点项目，曾获得北京市科学技术奖二等奖1项。

摘      要：

          In this talk we discuss quasi-neutral limit and the small Debye length structure stability problem of PNP-NS equations for electro-hydrodynamics. Quasi-neutrality is one basic assumption in physics such as semiconductors and plasma, which is firstly proposed by W.Van Roosbroech in Bell System Tech. J., 1950. We prove the small debye length quasi-neutral limit of the initial-boundary value problem for PNP-NS system for physicochemical hydrodynamics with the differential diffusion coefficients for two kinds of charges and the general ill-prepared smooth initial data, and obtain the convergence rate of the approximating solution having the form of the boundary layer, the initial layer and the mixed layer to the the exact solution of the system when the Debye length tends to zero, where the mixed layer functions have only the algebraic decay rates with respect to the fast variables. Thus, the rigorous quasineutrality theory of the electric-diffusion of ions in physicochemical hydrodynamics is established.

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