Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1783-1807.doi: 10.1007/s10473-020-0612-9

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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).

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

CLC Number: 

  • 76N10
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