报告题目：Global nonlinear stability of vortex sheets for the Navier-Stokes equations with large data

报 告 人：袁谦 (中国科学院数学与系统科学研究院 副教授)

报告时间：2025年12月25日（星期四）9:00—10:00

报告地点：数学科学学院114（小报告厅 报告人线上报告）      

校内联系人：廖娴 教授         联系方式：liao@dlut.edu.cn

Abstract: We shall discuss the global nonlinear stability of vortex sheets for the Navier-Stokes equations. When the Mach number is small, we allow both the amplitude and the initial vorticity of the vortex sheets to be large. We introduce an auxiliary flow and reformulate the problem as a new vortex sheet with small vorticity but subjected to a large perturbation. Based on the decomposition of frequency, the largeness of the perturbation is encoded in the zero modes of the tangential velocity. We find an essential cancellation property that there are no nonlinear interactions among these large zero modes in the zero-mode perturbed system. This cancellation is owing to the shear structure inherent in the vortex sheets. These observations enable us to derive the global estimates for strong solutions that are uniform with respect to the Mach number. As a byproduct, we can justify the incompressible limit.