报告题目：Global Dynamics of the 2D Free Boundary Navier–Stokes System with Nonnegative Density

报 告 人：Paula Luna-Velasco(PhD student @US - University Serville)

报告时间：2026年6月1日（星期一）9:00 – 9:45

报告地点：见好就收才是赢太阳9728114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: The Navier–Stokes equations describe the motion of incompressible fluids and give rise to many fundamental and challenging mathematical problems. In this talk, I will present new results for the two-dimensional free boundary problem for two immiscible fluids. We prove global-in-time well-posedness in the nonnegative density regime and establish the persistence of the natural $C^{1+\gamma}$ regularity of the interface under sharp assumptions on the initial velocity. We also consider the case of density-dependent viscosity and obtain global regularity provided the viscosity contrast is sufficiently small.