Small Scale Formations in the Incompressible Porous Media Equation

Authors

Kiselev, A; Yao, Y

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.

Citation

Kiselev, A., and Y. Yao. “Small Scale Formations in the Incompressible Porous Media Equation.” Archive for Rational Mechanics and Analysis 247, no. 1 (February 1, 2023). https://doi.org/10.1007/s00205-022-01830-z.
Archive for Rational Mechanics and Analysis

Publication Links