报告题目: Nonlinear stability of compressible vortex sheets in three-dimensional elastodynamics

报告人：袁迪凡（北京师范大学）

邀请人&主持人：黄辉

报告时间与地点：2025年10月25日（周六）下午16:00—17:00，国产主播 425室

报告摘要: In this talk, I will show nonlinear stability and existence of compressible vortex sheet solutions for three-dimensional isentropic elastic flows. This problem involves a nonlinear hyperbolic system with a characteristic free boundary. The major novelty of our approach includes the following two key aspects: (1) For the three-dimensional compressible Euler vortex sheets, the front symbol exhibits degenerate ellipticity in certain frequency directions, which makes it challenging to ensure the front’s regularity. Our analysis reveals that the non-parallel structure of the deformation gradient tensor plays a crucial role in recovering ellipticity in the front symbol, thereby enhancing the regularity of the free interface. (2) Another significant challenge in three dimensions arises from the strong degeneracy caused by the collision of repeated roots and poles. To resolve this, we refine Coulombel’s diagonalization framework and construct a suitable transformation that reduces the degeneracy order of the Lopatinskii matrix. Finally, we establish the local existence and nonlinear stability of vortex sheets showing stability within a subsonic regime. This is a joint work with Ming Chen, Feimin Huang and Dehua Wang.

报告人介绍：袁迪凡，北师大副研究员，博士毕业于中科院，博士期间公派美国匹兹堡大学，先后在香港城市大学，意大利布雷西亚大学，英国牛津大学从事博士后研究，主要研究流体力学方程数学理论，相关工作发表在CPAM, ARMA，JMPA等学术期刊。