中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人：王振富 助理教授 (北京国际数学研究中心)
题 目：Mean Field Limit and Quantitative Estimates with Singular Attractive Kernels
时 间：2020.12.4(星期五), 9:00-10:00
地 点：数学院南楼N224室
摘 要：We study the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. Joint work with D. Bresch and P.-E. Jabin.
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报告人：赵文彬 访问助理教授 (北京大学)
题 目：Compressible dissipative elastodynamics systems with zero shear viscosity
时 间：2020.12.4(星期五), 10:00-11:00
地 点：数学院南楼N224室
摘 要：In this talk, we discuss compressible dissipative elastodynamics systems with zero shear viscosity, and prove global stability around a constant equilibrium. Due to the low pointwise dispersive estimate for the divergence-free projection of solutions, and the lack of null structures in convective terms, energy estimates, combined with Green’s functions and dispersive estimates, for both solutions and their potentials, are obtained to control the interactions in nonlinear terms. This is joint work with Prof. HU Xianpeng from City University of Hong Kong.
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