报告题目:Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains

报告人：谈进 博士（Cergy-Paris University）

报告时间：2024年1月12日（周五）下午14:00-15:00

报告地点：理A110

摘要：In a well-known book of P.-L. Lions, global existence results for finite energy weak solutions of the inhomogeneous incompressible Navier-Stokes equations (INS) were proved without assuming positive lower bounds on the initial density, hence allowing for vacuum. Uniqueness, regularity of Lions’ weak solutions and persistence of boundary regularity of density patches were listed as open problems. In the case where the fluid domain is either bounded or the torus, Lions’problem has been understood well nowadays. However, the case of unbounded domains was left open. In this talk, I will present some regularity and uniqueness results of Lions’ weak solutions for (INS) with additional regularity only assumed for the initial velocity, in the whole space case. As an application, I will explain how these results imply persistence of boundary regularity of a density patch and a vacuum bubble in the whole space. The talk is based on a recent work with my mentor Christophe Prange (CY Cergy Paris University).

报告人简介：谈进，博士，2021年9月博士毕业于法国巴黎东大（UPEC），2021年9月至今在Cergy Paris University从事博士后研究工作，研究兴趣为流体动力学和磁流体动力学中的偏微分方程，其研究受到多项资助（包括 Post-doc funding from project CY Nonlinear Analysis、 INSMI 、ANR project BORDS等），研究成果接收发表在CMP，CPDE，M3AS，JDE、JMFM、 Commun. Contemp. Math.等。

邀请人：王彦霖