Abstract
We study a quasilinear parabolic curl system, which comes from a time-dependent version of the elliptic system of the Meissner state of a type II superconductor subjected to an applied magnetic field. We examine both the initial-boundary value problem in a bounded three dimensional domain and the Cauchy problem in \BbbR 3. Local existence and regularity of the solutions are proved, and the global solutions of the Cauchy problem are obtained for small data.
| Original language | English |
|---|---|
| Pages (from-to) | 6471-6516 |
| Number of pages | 46 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 53 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2021 |
Bibliographical note
Funding Information:\ast Received by the editors July 9, 2020; accepted for publication (in revised form) August 26, 2021; published electronically November 18, 2021. https://doi.org/10.1137/20M1351643 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the first author was partially supported by NRF-2019R1A2C1084685 and NRF-2015R1A5A1009350. The work of the second author was partially supported by the National Natural Science Foundation of China grants 12071142 and 11671143, and by the research grants UDF01001805 and CUHKSZWDZC0003. \dagger Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea (kkang@yonsei.ac.kr). \ddagger School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen 518172, Guangdong, China, and School of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China (panxingbin@cuhk.edu.cn, xbpan@math.ecnu.edu.cn).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics
All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics