The Incompressible Porous Media equation: well-posedness and relaxation approximation

par Timothée Crin-Barat

mardi 19 nov. 2024, 11:15 → 12:15 Europe/Paris

Amphi Schwartz (IMT)

In this joint work with Roberta Bianchini and Marius Paicu, we address the existence of stably stratified solutions to the Incompressible Porous Media (IPM) equation. In particular, we justify the nonlinear asymptotic stability for initial perturbations in $\text{Missing argument for dot}$H^3$. Moreover, we justify the strong relaxation limit of the Boussinesq system with damped velocity towards the (IPM) equation under a suitable scaling. A crucial part of our analysis relies on the use of an anisotropic Littlewood-Paley decomposition to derive new bounds on the vorticity.