THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

doi:10.1007/s10473-020-0612-9

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

THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

穆鹏程¹, 琚强昌²

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. 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/Abstract

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

穆鹏程, 琚强昌. THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS[J]. 数学物理学报(英文版), 2020, 40(6): 1783-1807.

Pengcheng MU, Qiangchang JU. THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS[J]. Acta mathematica scientia,Series B, 2020, 40(6): 1783-1807.

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THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

THE CAUCHY PROBLEM FOR THE TWO LAYER VISCOUS SHALLOW WATER EQUATIONS

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