The Muskat problem with $C^1$ data
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- by Ke Chen, Quoc-Hung Nguyen and Yiran Xu PDF
- Trans. Amer. Math. Soc. 375 (2022), 3039-3060 Request permission
Abstract:
In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in $\dot C^1(\mathbb {R}^d)\cap L^2(\mathbb {R}^d)$.References
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Additional Information
- Ke Chen
- Affiliation: Fudan University, 220 Handan Road, Shanghai 200433, China
- ORCID: 0000-0002-4560-2107
- Email: kchen18@fudan.edu.cn
- Quoc-Hung Nguyen
- Affiliation: ShanghaiTech University, 393 Middle Huaxia Road, Shanghai 201210, China
- Address at time of publication: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- Email: qhnguyen@amss.ac.cn
- Yiran Xu
- Affiliation: Fudan University, 220 Handan Road, Shanghai 200433, People’s Republic of China
- Email: yrxu20@fudan.edu.cn
- Received by editor(s): April 28, 2021
- Published electronically: February 9, 2022
- Additional Notes: The second author was supported by the ShanghaiTech University startup fund and the National Natural Science Foundation of China (12050410257). This work was finished during Ke Chen and Yiran Xu’s visit to ShanghaiTech.
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 3039-3060
- MSC (2020): Primary 35Q35, 76S05
- DOI: https://doi.org/10.1090/tran/8559
- MathSciNet review: 4402655