Global regularity for 2D Navier-Stokes free boundary with small viscosity contrast
数学专题报告
报告题目(Title)： Global regularity for 2D Navier-Stokes free boundary with small viscosity contrast
报告人(Speaker)：Francisco Gancedo 教授 (Universidad de Sevilla，Spain)
地点(Place)：Zoom 会议 ID： 846 607 95312, 密码：770833
时间(Time)： 2022 年 04 月 20 日（周三） 15:00--16:00
邀请人(Inviter)：薛留堂
报告摘要
We study the dynamics of two incompressible immiscible fluids in 2D modeled by the inhomogeneous Navier-Stokes equations. We show a new approach to prove that if initially the viscosity contrast is small then there is global-in-time regularity. The result allows to obtain preservation of the natural C1+γ Hölder regularity of the interface for all 0 < γ < 1 with low Sobolev regularity of the initial velocity without any extra technicality. In particular, it uses new quantitative harmonic analysis bounds for Cγ norms of even singular integral operators on characteristic functions of C1+γ domains.
