数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1783-1807.doi: 10.1007/s10473-020-0612-9

• 论文 • 上一篇    下一篇

THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

穆鹏程1, 琚强昌2   

  1. 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2019-07-08 修回日期:2020-05-17 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Qiangchang JU,E-mail:ju_qiangchang@iapcm.ac.cn E-mail:ju_qiangchang@iapcm.ac.cn
  • 作者简介:Pengcheng MU,E-mail:mupc288
  • 基金资助:
    Ju was supported by the NSFC (11571046, 11671225), the ISF-NSFC joint research program NSFC (11761141008) and the BJNSF (1182004).

THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

Pengcheng MU1, Qiangchang JU2   

  1. 1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2019-07-08 Revised:2020-05-17 Online:2020-12-25 Published:2020-12-30
  • Contact: Qiangchang JU,E-mail:ju_qiangchang@iapcm.ac.cn E-mail:ju_qiangchang@iapcm.ac.cn
  • Supported by:
    Ju was supported by the NSFC (11571046, 11671225), the ISF-NSFC joint research program NSFC (11761141008) and the BJNSF (1182004).

摘要: In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs' regularization method.

关键词: two layer shallow water equations, global strong solution, hybrid Besov spaces

Abstract: In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs' regularization method.

Key words: two layer shallow water equations, global strong solution, hybrid Besov spaces

中图分类号: 

  • 76N10