Timothée Crin-Barat (Toulouse)

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

In this joint work with Roberta Bianchini and Marius Paicu, we investigate the existence of stably stratified solutions to the Incompressible Porous Media (IPM) equation and establish their nonlinear asymptotic stability for initial perturbations in $\dot H^{3+}$. In addition, we rigorously justify the strong relaxation limit of the stratified Boussinesq system with velocity damping toward the (IPM) equation. Our analysis relies on an anisotropic Littlewood–Paley framework, which enables us to lower the regularity requirement on the initial data to obtain Lipschitz-type bound on the vorticity.