Small scale formations in the incompressible porous media equation

Alexander Kiselev; Yao Yao

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Small scale formations in the incompressible porous media equation

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arxiv 2102.05213 v1 pith:MWRA5TWP submitted 2021-02-10 math.AP

Small scale formations in the incompressible porous media equation

Alexander Kiselev , Yao Yao This is my paper

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keywords equationincompressiblemediaporousallowsapplicationclassconstruct

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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.

Small scale formations in the incompressible porous media equation

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