Local Existence of Classical Solution to the Chemotaxis‐Shallow Water System With Vacuum in ℝ2
ABSTRACT 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.
Authors
- Li Chen (ORCID: https://orcid.org/0000-0003-4135-6401)
- Zhen Luo (ORCID: https://orcid.org/0000-0001-8621-0874)
- Y. Wang (ORCID: https://orcid.org/0009-0009-1397-1280)
Institutions
- Technische Hochschule Mannheim (DE)
- Shanghai University (CN)
- University of Mannheim (DE)
- Xiamen University (CN)
Publication Details
- Journal
- Mathematical Methods in the Applied Sciences
- Published
- 2025-11-06
- DOI
- https://doi.org/10.1002/mma.70260
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 0.00