Seminario EDP UAM-ICMAT
Sharp asymptotic stability of the incompressible porous media equation
Ponente: Shan Wang (ICMAT)Fecha: viernes 20 de febrero de 2026 - 12:30Lugar: Aula Gris 1, ICMAT
Resumen:
In this talk, we show the asymptotic stability of the incompressible porous media (IPM) equation near a stable stratified density for initial perturbations in the Sobolev space \(H^2\)\(^+\). While it is known that such a steady state is unstable in \(H^2\), our result establishes a sharp stability threshold in higher-order Sobolev spaces. On the other hand, we introduce the anisotropic commutator estimates, which can be applied to consider the stability of the (IPM) system in the anisotropic Besov space.
