Mild ill-posedness in $W^{1,\infty}$ for the incompressible porous media
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Mild ill-posedness in $W^{1,\infty}$ for the incompressible porous media
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In this paper, we investigate the perturbation problem of the incompressible porous media (IPM) equation on the whole space $\mathbb{R}^2$. We prove the mild ill-posedness of IPM equation in the critical space $W^{1,\infty}$ when the initial data are small perturbations of the more general stable profile $g(x_2),$ and accordingly, instability …