Asymptotic stability of the incompressible porous media equation holds in H^k for every k>2, with L2 convergence to the measure-preserving stratification at rate t^{-k/2}, and the threshold is sharp.
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Sharp asymptotic stability of the incompressible porous media equation
Asymptotic stability of the incompressible porous media equation holds in H^k for every k>2, with L2 convergence to the measure-preserving stratification at rate t^{-k/2}, and the threshold is sharp.