We consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators.

中文翻译：

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分数多孔介质流的经典解决方案

我们考虑了Caffarelli和Vazquez（2011）引入的分数多孔介质流，并获得了局部存在的时间，唯一性和用于光滑解的爆破准则。该证明基于建立涉及分数次拉普拉斯算子的换向器估计。