Small scale formations in the incompressible porous media equation

Published 10 Feb 2021 in math.AP | (2102.05213v1)

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.

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