Non-uniform dependence on initial data for the modified μ-Camassa-Holm equation

Considered herein is the initial value problem for the modified μ-Camassa-Holm equation. It is shown that the solution map of this problem is not uniformly continuous in Sobolev spaces Hs(S) for s>5/2 on the circle. Based on the well-posedness result and the lifespan for this problem, the method of approximate solutions is utilized.