Small scale formations in the incompressible porous media equation

Abstract

We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an application, this allows us to obtain nonlinear instability for a class of stratified steady states of IPM.

21 pages, 3 figures

References in corpus (1)

• Infinite superlinear growth of the gradient for the two-dimensional Euler equation

Cited by in corpus (1)

• Well-posedness of the Stokes-transport system in bounded domains and in the infinite strip