Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The Muskat problem with $C^1$ data
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 35Q35, 76S05
  • Retrieve articles in all journals with MSC (2020): 35Q35, 76S05
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鈥檚 Republic of China
  • Email: qhnguyen@amss.ac.cn
  • Yiran Xu
  • Affiliation: Fudan University, 220 Handan Road, Shanghai 200433, People鈥檚 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鈥檚 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