"à la Hoff" solutions for compressible Navier-Stokes equations in 1D

par M. Pierre Gonin-Joubert

lundi 19 janv. 2026, 10:30 → 11:30 Europe/Paris

Fokko du Cloux (ICJ)

Navier-Stokes equations are partial differential equations describing the motion of pure fluids. Although they have been studied extensively by mathematicians for a century, they have yet to reveal all their secrets. In this presentation, we will begin with an overview of the world of elliptic, parabolic, and hyperbolic PDEs in order to understand the behavior behind each of them. We will use these simplified models to understand several systems of 1D Navier-Stokes equations. The questions asked will be fundamental: what are the techniques for constructing solutions? Do we have uniqueness? We will emphasize the regularity assumptions of the initial conditions and present the framework of “à la Hoff” solutions. Briefly, we will explain how this framework is relevant to the study of fluid mixture dynamics.