Analysis reveals local existence of classical solutions in chemotaxis‐shallow water systems, suggesting broader implications for vacuum conditions.
In this paper, we consider the chemotaxis‐shallow water system in . 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 nonvacuum. The initial data is allowed vacuum and the spatial measure of the set of vacuum can be arbitrarily large.
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Chen et al. (2025) studied this question.
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