中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
杰出访问研究员报告
Speaker: 郏浩（明尼苏达大学）
Inviter: 付保华
Language: English
Title: Global wellposedness of the dynamical Prandtl equation
Time & Venue: 2026年9月22日（星期二）10:30-11:30 南楼N913
Abstract: The Prandtl equation was first derived by L. Prandtl in 1904 as the limiting equation, in the vanishing viscosity limit of the Navier–Stokes equation around an obstacle. Since then, it has played a fundamental role in understanding the dynamics of fluid flow at high Reynolds numbers in the presence of a physical boundary. The rigorous analysis of the Prandtl equation was pioneered by Oleinik, who proved the first global wellposedness for the steady Prandtl equation, and local wellposedness for the dynamical (or unsteady) Prandtl equation, under suitable natural monotonicity and pressure assumptions. An important question, raised already by Oleinik, is whether one can extend the local wellposedness to global wellposedness under natural monotonicity and pressure conditions. In a recent work joint with Zhen Lei and Cheng Yuan, building on significant earlier work of Xin-Zhang and Xin-Zhang-Zhao, we provided a proof of the global wellposedness of classical solutions to the dynamical Prandtl equations. We also allow our initial and inflow data to assume any of the three physically significant matching rates: polynomial, exponential and Gaussian. In the talk, I will briefly explain the physical motivations of the Prandtl equation, outline the main steps of the proof, and if time permits, discuss some expected but technically quite nontrivial aspects of the wellposedness theory including the construction of compatible data for the approximating system and high order energy estimates in the presence of a boundary.
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