报告题目：Structural stability of Prandtl boundary layers in the entire subsonic regime

报 告 人：张筑（香港理工大学）

报告时间：2025年4月18日  16:30

报告地点：格物楼528

报告摘要：

Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively studied incompressible fluid dynamics in two dimensions. This paper aims to establish the structural stability of boundary layer profiles in the form of shear flow for the two-dimensional steady compressible Navier-Stokes equations. Our estimates are uniform across the entire subsonic regime, where the Mach number $m\in (0.1)$. As a byproduct, we provide the first result concerning the low Mach number limit in the presence of Prandtl boundary layers. The proof relies on the quasi-compressible-Stokes iteration, along with a subtle analysis of the interplay between density and velocity variables in different frequency regimes, and the identification of cancellations in higher-order estimates.

报告人简介：

张筑，2019年毕业于香港中文大学，2019-2022香港城市大学博士后，现于香港理工大学任助理教授。研究方向为流体力学边界层和动力学方程。成果发表在Arch. Ration. Mech..Anal.、J. Math.Pure Appl.等期刊。现主持香港研究资助局项目两项。