In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from product Sobolev spaces Hˢ × Hˢ to C([0,T]; Hˢ × Hˢ). The proof of nonuniform dependence is based upon approximate solutions.
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Ryan C. Thompson (2024) studied this question.
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