Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density

报告题目： Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density

报 告 人： 邵峰， 北京大学

时    间： 2025年07月02日（星期三）14:30-15:30

地    点： 思源楼525

摘    要： In this talk, I will discuss the global well-posedness of 2-D inhomogeneous Navier-Stokes equations (INS) with bounded density. We solve Lions' density patch problem about the preseving of boundary regularity of a density patch and Lions' open problem on the 2-D uniqueness of weak solutions if the density has a positive lower bound. Particularly, our proof of uniqueness is based on a duality argument and a surprising finding that the estimate $t^{1/2}\nabla u\in L^2(0,T; L^\infty(\mathbb R^d))$ instead of $\nabla u\in L^1(0, T; L^\infty(\mathbb R^d))$ is enough to ensure the uniqueness of the solution. This talk is based on joint works with Tiantian Hao, Dongyi Wei and Zhifei Zhang.