Weak entropy solution for a Keller-Segel type fluid model

Li Chen; Feimin Huang; Lingjun Liu

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arXiv · 2108.04721

Weak entropy solution for a Keller-Segel type fluid model

Li Chen·Feimin Huang·Lingjun Liu

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Abstract

In this paper, we consider a Keller-Segel type fluid model, which is a kind of Euler-Poisson system with a self-gravitational force. We show that similar to the parabolic case, there is a critical mass $8\pi$ such that if the initial total mass $M$ is supercritical, i.e., $M> 8\pi$, then any weak entropy solution with the same mass $M$ must blow up in finite time. The a priori estimates of weak entropy solutions for critical mass $M=8\pi$ and subcritical mass $M<8\pi$ are also obtained.

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Li Chen, Feimin Huang, Lingjun Liu. 2021-08-10. Weak entropy solution for a Keller-Segel type fluid model. https://arxiv.org/abs/2108.04721

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