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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