Small scale formations in the incompressible porous media equation
Analysis of PDEs
2021-02-11 v1
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.
Keywords
Cite
@article{arxiv.2102.05213,
title = {Small scale formations in the incompressible porous media equation},
author = {Alexander Kiselev and Yao Yao},
journal= {arXiv preprint arXiv:2102.05213},
year = {2021}
}
Comments
21 pages, 3 figures