中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人： Prof. Igor Kukavica（University of Southern California）
题  目：On the inviscid limit for the Navier-Stokes equations
时  间：2022.03.04（星期五），00:00-01:00
地  点：Zoom会议：924 888 5804    密码：AMSS2022
摘  要：The question of whether the solution of the Navier-Stokes equation converges to the solution of the Euler equation as the viscosity vanishes is one of the fundamental problems in fluid dynamics. In the talk, we will review current results on this problem. We will also present a recent result, joint with Vlad Vicol and Fei Wang, which shows that the inviscid limit holds for the initial data that is analytic only close to the boundary of the domain, and has Sobolev regularity in the interior.

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报告人： Prof. Mitia Duerinckx（Paris-Saclay University  ）
题  目：Effective viscosity of dilute suspensions
时  间：2022.03.10（星期四），21:00-22:00
地  点：Zoom会议：924 888 5804    密码：AMSS2022
摘  要：In this talk, based on joint work with A.Gloria, I will investigate the large-scale rheology of systems of suspended particles in fluids. After reviewing our recent results on the definition of the effective viscosity of such systems in terms of homogenization theory, I will focus on its asymptotic expansion in dilute regime: I will present a new, fully optimal proof of Einstein's viscosity formula for the first-order expansion and show how to pursue the asymptotic expansion to higher orders. The essential difficulty originates in the long-range nature of hydrodynamic interactions: these require suitable renormalizations, which are best expressed by means diagrammatic expansions.