周期情形下两分支Camassa-Holm系统解对初值的不一致依赖性

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

利用近似解方法和解的局部适定性结果,讨论了一个周期情形下两分支Camassa-Holm系统Cauchy问题解在Besov空间B2,1^3/2(T)×B2,1^3/2(T)中对初值的不一致连续依赖性。该方法还可以用来讨论其他非线性发展方程解对初值的不一致连续依赖性。

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 B2,1^3/2(T)×B2,1^3/2(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.