Non-uniform dependence for the periodic higher dimensional Camassa-Holm equations

作者：Zhao, Yongye^*; Yang, Meiling; Li, Yongsheng

来源：Journal of Mathematical Analysis and Applications, 2018, 461(1): 59-73.

DOI：10.1016/j.jmaa.2018.01.012

• Higher dimensional Camassa-Holm equations
• Transport equation
• Besov spaces
• Non-uniform dependence

In this paper, we investigate the dependence on initial data of solutions to the higher dimensional Camassa-Holm equations with periodic boundary condition in Besov spaces. We show that when s > 1 + d/2 (d >= 2) and 1 <= r <= infinity, the solution map is not uniformly continuous from B-2,r(s)(T-d) into C ([0,T]; B-2,r(s)(T-d)) for r < infinity or from B-2,r(s)(T-d) into L-infinity ([0, T]; B-2,r(s)(T-d)) for r = infinity.

• 出版日期2018-5-1
• 单位华南理工大学; 广州航海学院