THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM

doi:10.1007/s10473-021-0113-5

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (1): 231-240.doi: 10.1007/s10473-021-0113-5

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THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM

Jishan FAN¹, Fucai LI², Gen NAKAMURA³

1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China;
2. Department of Mathematics, Nanjing University, Nanjing 210093, China;
3. Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Received:2019-12-24 Revised:2020-09-12 Online:2021-02-25 Published:2021-04-06
Contact: Fucai LI E-mail:fli@nju.edu.cn
About author:Jishan FAN,E-mail:fanjishan@njfu.edu.cn;Gen NAKAMURA,E-mail:fanjishan@njfu.edu.cn
Supported by:
Fan was supported by NSFC (11971234). Li was supported in part by NSFC (11671193), and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Abstract

Abstract: In this paper we prove the local well-posedness of strong solutions to a chemotaxis-shallow water system with initial vacuum in a bounded domain $\Omega\subset\mathbb{R}^2$ without the standard compatibility condition for the initial data. This improves some results obtained in [J. Differential Equations 261(2016), 6758-6789].

Key words: chemotaxis, shallow water, vacuum, local well-posedness, strong solution

CLC Number:

92C17

Jishan FAN, Fucai LI, Gen NAKAMURA. THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM[J].Acta mathematica scientia,Series B, 2021, 41(1): 231-240.

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References

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THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM

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