中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人：诸葛金平 博士（University of Chicago）
题 目：Large-scale regularity for stationary Navier-Stokes equations over non-Lipschitz boundaries
时 间：2021.07.07（星期三），10:00-12:00
地 点：腾讯会议：304 706 305
摘 要：In this talk, I will discuss the large-scale boundary regularity of the stationary Navier-Stokes equations over a microscopically oscillating John boundary (with a no-slip boundary condition), which allows inward cusps or fractals. By a comprehensive large-scale analysis, we show a large-scale Lipschitz estimate for the velocity and a large-scale oscillation estimate for the pressure. By introducing the 1st-order and 2nd-order boundary layers, we also show the large-scale C^{1,alpha} and C^{2,alpha} estimates (For C^{2,alpha} estimate, we assume additionally the boundary is periodic). The proofs rely on the quantitative excess decay method developed recently in homogenization theory. This is joint work with Mitsuo Higaki and Christophe Prange.
--------------------------------------------------------
报告人：郑凡 博士（Instituto de Ciencias Matem´aticas, Madrid, Spain）
题 目：若干非线性方程的长时间适定性
时 间：2021.07.09（星期五），15:00-17:00
地 点：腾讯会议：450 197 853
摘 要：In this talk I will continue the application of the normal form method to various interesting equations such as the Euler-Poisson equation, the water wave equation and the Burgers-Hilbert equation. New ingredients of the proof will be introduced along the way.
附件：