Dynamics of singularity surfaces for the compressible viscous fluids
数学专题报告
报告题目(Title)：Dynamics of singularity surfaces for the compressible viscous fluids
报告人(Speaker)：Marcel Zodji (University of Évry, France)
地点(Place)：Zoom ID: 818 521 62485 Password: 123456
时间(Time)：2025年11月12日（周三）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
The motion of a compressible viscous fluid is described by the Navier-Stokes system. It is a system of hyperbolic-parabolic mixed-type PDEs. In this talk, we will study the so-called density patch problem: If we are given a density that is initially "regular" on both sides of a hypersurface across which it is discontinuous, will this structure be preserved over time?
An important quantity in the mathematical analysis of this system is the so-called effective flux, which was discovered by Hoff and Smoller (1985). More precisely, the mathematical properties of this quantity play a crucial role in the study of the propagation of oscillations in compressible fluids [Serre, 1991], in the construction of weak solutions [P-L Lions, 1996] or the propagation of discontinuity surfaces [Hoff, 2002], to cite just a few examples.
In the case of density-dependent viscosities, the behavior of the effective flux degenerates, which renders the analysis more subtle.
