JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 42-49.doi: 10.6040/j.issn.1671-9352.0.2019.125

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Non-uniform dependence on initial data for the periodic two-coupled Camassa-Holm system

WANG Hai-quan   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: Considered herein is the initial value problem for the periodic two-coupled Camassa-Holm system. It is shown that the solution map of this problem is not uniformly continuous in Besov spaces B3/22,1(T)×B3/22,1(T). Based on the well-posedness result and the lifespan for this problem, the method of approximate solutions is utilized. The same approach can be used to discuss this property of the solutions for the other nonlinear partial differential equations.

Key words: the periodic two-coupled Camassa-Holm system, non-uniform dependence, Besov spaces, approximate solutions

CLC Number: 

  • O175.2
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