Abstract
ABSTRACT Considered herein is the Cauchy problem of the two-component Novikov system with peakons. Based on the local well-posedness results for this problem, it is shown that the solution map of this problem on the line is not uniformly continuous in Besov spaces with through the method of approximate solutions. Next, in the periodic case, the non-uniform continuity of the solution map in Besov spaces and Hölder spaces with is discussed. Finally, the Hölder continuity of this solution map in Sobolev spaces is investigated.
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