数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
6期
1781-1794
,共14页
modified Camassa-Holm equation%Cauchy problem%non-uniform continuity%Sobolev spaces
In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt+umx+2uxm=0, m=(1??2x)2u, u(x, 0)=u0(x)∈Hs(R), x∈R, t>0, and show that the solution map is not uniformly continuous in Sobolev spaces Hs(R) for s > 7/2. Compared with the periodic problem, the non-periodic problem is more di?cult, e.g., it depends on the conservation law. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part.
