Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 427-441.

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Global Weak Solutions to a High-Order Camass-Holm Type Equation

Kexin Luo1,*(),Shaoyong Lai2   

  1. 1 School of Science, Xihua University, Chengdu 610039
    2 Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130
  • Received:2021-04-15 Online:2022-04-26 Published:2022-04-18
  • Contact: Kexin Luo E-mail:luokexin0122@163.com
  • Supported by:
    the NSFC(11471263);the Xihua Award(2021190)

Abstract:

The viscous approximation technique is employed to investigate the existence of global weak solutions for a high-order Camassa-Holm type equation. A higher integrability estimate of the viscous solutions for the equation and the upper bound estimate on the space derivative of its viscous solutions are derived to prove the existence.

Key words: Global weak solutions, Viscous approximations, Camassa-Holm-type equation

CLC Number: 

  • O175.29
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