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
偏微分方程研讨班
Speaker: 高宸（中国科学技术大学）
Inviter: 张立群
Language: Chinese
Title: Global existence and stability of semi-self-similar solutions of the 2D Prandtl equation
Time & Venue: 2026年6月4日（星期四）14: 30-15: 30 & N208
Abstract: This talk will discuss the two-dimensional unsteady Prandtl system for stagnation flows. By introducing a semi-self-similar transformation, the problem reduces to a degenerate parabolic equation. Under suitable assumptions on the initial data, we prove the global existence of the semi-self-similar solution. Moreover, we establish the large-time behavior showing convergence to the steady self-similar solution by some ODE techniques. Finally, the stability of this semi-self-similar solution is proved via a bootstrap argument, provided the initial perturbation is sufficiently small.
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Speaker: 袁诚（复旦大学）
Inviter: 张立群
Language: Chinese
Title: Boundary Regularity and Global Classical Solution of Dynamic Prandtl Equation
Time & Venue: 2026年6月4日（星期四）15: 30-16: 30 & N208
Abstract: In this talk, I will present the boundary regularity theory and the global well-posedness of classical solutions for the dynamic Prandtl equations in Sobolev framework.We first establish the up-to-boundary regularity theory for the Prandtl system. The main obstacle lies in the lack of an explicit expression and key symmetries for the fundamental solution of a Kolmogorov operator (which can be viewed as the linearized operator of Prandtl equation) in the half-space. Our key strategies include identifying the collaboration mechanism between diffusion and transport effect of Kolmogorov operator, and then combining Fourier analysis, enhanced dissipation theory, and iterative methods to establish a series of regularity estimates for linear and quasilinear equations. By combining the established boundary regularity with local solution theory, we also obtain the global well-posedness of regular classical solutions for the Prandtl system. This is joint work with Prof. Hao Jia (University of Minnesota) and Prof. Zhen Lei (Fudan University).
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