On the regularity of the solution map of the porous media equation

Hasan Inci

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arXiv · 1712.09204

On the regularity of the solution map of the porous media equation

Hasan Inci

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Abstract

In this paper we consider the incompressible porous media equation in the Sobolev spaces $H^s(\R^2), s > 2$. We prove that for $T > 0$ the time $T$ solution map $\rho_0 \mapsto \rho(T)$ is nowhere locally uniformly continuous. On the other hand we show that the particle trajectories are analytic curves in $\R^2$.

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Hasan Inci. 2017-12-26. On the regularity of the solution map of the porous media equation. https://arxiv.org/abs/1712.09204

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