Non-uniform dependence on initial data for the periodic Degasperis–Procesi equation

In this paper, we show that the solution map of the periodic Degasperis–Procesi equation is not uniformly continuous in Sobolev spaces Hs(T) for s>3/2. This extends previous result for s⩾2 to the whole range of s for which the local well-posedness is known. Our proof is based on the method of approximate solutions and well-posedness estimates for the actual solutions.