Global-in-time solutions for the Stokes-transport system

Seminario de Ecuaciones diferenciales by Elena Salguero (Max Planck Institute for Mathematics in the Sciences, Leipzig) Abstract:  The Stokes-transport system describes the evolution of a density scalar advected by a velocity field that satisfies the Stokes equation with gravitational forcing. This system of PDEs belongs to the class of active scalar equations and models the dynamics of highly viscous fluids with heterogeneous density. In this talk, we will combine a Lagrangian approach with harmonic analysis techniques to find global solutions for this system in 2D, with a focus on the case where the density takes two distinct constant values. This leads to a two-phase problem that models the evolution of two different immiscible fluids in a 2D domain.