学术报告报告主题1: 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（北京工业大学）
报告时间：2026年 9 月23日（星期三）下午3:00-4:00
报告地点：37号楼3A01
报告摘要：
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.
报告人介绍：
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。1998年南京大学博士毕业，后在中科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。
报告主题2: Optimal convergence estimate of the limit from inverse power potential to hard sphere Boltzmann equation
报 告 人: 周玉龙教授（中山大学）
报告时间：2026年 9 月23日（星期三）下午4:00-5:00
报告地点：37号楼3A01
报告摘要：
The inverse power potential U(r)=r^{-1/s}, 0<s<1, generates the Boltzmann kernel B^s = |v-v_*|^{1-4s} b_s(θ) with an angular singularity as θ → 0. Jang-Kepka-Nota-Velázquez [Vanishing angular singularity limit to the hardsphere Boltzmann equation, J. Stat. Phys., 190(4), 2023] proved the limit B^s → (1/4)|v-v_*| as s → 0, as well as weak convergence of solutions, but without a rate. In this work we establish the sharp estimate|b_s(θ) ? 1/4| ≤ C s θ^{?2?2s}. In particular, this sharp estimate yields the optimal O(s) convergence rate for solutions of the homogeneous Boltzmann equation with large initial data in suitable Sobolev spaces; i.e., for any t ∈ [0, T], we have f^s(t) = f^0(t) + O(s), quantified by the L^1_k norm for k ≥ 2.
报告人介绍：
周玉龙，中山大学教授、博士生导师，国家高层次人才，长期从事Boltzmann方程、Landau方程等动理学方程的理论研究，在相关领域取得了一系列重要成果，发表于Adv. Math.、CMP、ARMA、Math Ann.、JFA等国际知名学术期刊。
邀 请 人: 杨东成 副教授
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