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Mild ill-posedness in $W^{1,\infty}$ for the incompressible porous media equation by Xie, Yaowei; Yu, Huan is a scholarly article available to read on EtoBox.

What is Mild ill-posedness in $W^{1,\infty}$ for the incompressible porous media equation about?

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 can be inferred. It is emphasized that our result holds for any vertically layered density $g(x_2)$ without requirement on the sign of $g'(x_2).$

Author

Xie, Yaowei; Yu, Huan

Published

2024

Language

EN