Global existence of quasi-stratified solutions for the confined IPM equation

TL;DR

This paper proves the global existence of smooth, bounded density solutions for the inviscid incompressible porous media equation in a confined setting, using stability and special initial conditions.

Contribution

It introduces a novel approach leveraging stratified solution stability and initial perturbation structure to establish global existence in a confined domain.

Findings

Global smooth solutions with bounded density are proven to exist.

The method eliminates boundary term complications in energy estimates.

The approach applies to the inviscid incompressible porous media equation.

Abstract

In this paper, we consider a confined physical scenario to prove global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the stability of stratified solutions, combined with an additional structure of our initial perturbation, which allows us to get rid of the boundary terms in the energy estimates.