The non-homogeneous Euler equations below the Lipschitz threshold
数学专题报告
报告题目(Title)：The non-homogeneous Euler equations below the Lipschitz threshold
报告人(Speaker)：Prof. Francesco Fanelli (Basque Center for Applied Mathematics, Spain)
地点(Place)：Zoom ID: 83757101893 Password: 123456
时间(Time)：2025年11月26日（周三）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
The incompressible Euler equations are well-known to be globally well-posed in the case of space dimension d=2, both in the strong solutions framework and in the Yudovich framework. No results of that kind are known for the non-homogeneous (that is, density-dependent) incompressible Euler system. In this talk, we show that both problems (i.e., global well-posedness and theory \`a la Yudovich for the density-dependent case) can be reduced to the study of a non-linear geometric quantity, which encodes the regularity of the velocity field along the level lines of the density. Such a geometric regularity places itself below the Lipschitz threshold.
