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. Armin Schikorra（University of Pittsburgh）
题 目：On Calderon-Zygmund type estimates for nonlocal PDE
时 间：2022.03.31（星期四）21:00-22:00
地 点：Zoom 会议号：924 888 5804 密码：AMSS2022
摘 要：I will report on progress obtained for the W^{s,p}-regularity theory for nonlocal/fractional equations of differential order 2s with bounded measurable Kernel. Namely, under (not yet optimal) assumptions on the kernel we obtain W^{t,p}-estimates for suitable right-hand sides, where s< t < 2s. Technically we compare such equations via a commutator estimate to a simpler fractional equation. Based on joint works with M. Fall, T. Mengesha, S. Yeepo.
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报告人： Prof. Konstantina Trivisa（University of Maryland）
题 目：Invariant measures for the stochastic Navier-Stokes Equations for compressible flows and the problem of turbulence
时 间：2022.04.07（星期四）21:00-22:00
地 点：Zoom 会议号：924 888 5804 密码：AMSS2022
摘 要：In this talk I'll present results on the long-time behavior of solutions to a stochastically forced Navier-Stokes system, describing the motion of a compressible viscous fluid. In the one dimensional case, the existence of an invariant measure for the Markov process generated by strong solutions was established in collaboration with Michele Coti-Zelati and Nathan Glatt-Holtz. In that work, we overcome the difficulties of working with non-Feller Markov semigroups on non-complete metric spaces by generalizing the classical Krylov-Bogoliubov method, and by providing suitable polynomial and exponential moment bounds on the solution, together with pathwise estimates. The talk will conclude with a discussion on some recent developments on the multi-dimensional case for related models.
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