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arXiv · 2403.01884

Local existence of classical solution to the chemotaxis-shallow water system with vacuum in $\mathbb{R}^2$

Li Chen·Zhen Luo·Yucheng Wang
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Abstract

In this paper, we consider the chemotaxis-shallow water system in $\mathbb{R}^2$. We establish the local existence of classical solution without assuming the initial height is small or has a small perturbation near a constant. The far field behavior of the height is a constant which could be either vacuum or non-vacuum. The initial data is allowed vacuum and the spatial measure of the set of vacuum can be arbitrarily large.

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Li Chen, Zhen Luo, Yucheng Wang. 2024-03-04. Local existence of classical solution to the chemotaxis-shallow water system with vacuum in $\mathbb{R}^2$. https://arxiv.org/abs/2403.01884

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