Small Scale Formations in the Incompressible Porous Media Equation
Archive for Rational Mechanics and Analysis（2022）
摘要
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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关键词
porous media equation,porous media,small scale formations,incompressible
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