BCAM, Thursday, December 18th, 2025, 17:00--18:00
Title: The non-homogeneous Euler equations below the Lipschitz threshold
Francesco Fanelli - BCAM
The incompressible Euler equations are well-known to be globally well-posed in the case of space dimension 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 à 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.