Finite time singularities of smooth solutions for the 2D incompressible porous media (IPM) equation with a smooth source

Abstract

We establish the existence of smooth, finite-energy solutions to the 2D incompressible porous media equation (IPM), with a compactly supported uniformly smooth source, which develop singularities in finite time.

54 pages. Minor corrections and comments added

Cited by in corpus (1)

• Finite time blow-up in a 1D model of the incompressible porous media equation