Considered herein is the initial value problem for the two-component Novikov system with peakons. Based on the local well-posedness results for this problem, it is shown that the solution map \(z_{0}\mapsto z(t)\) of this problem in the periodic case is not uniformly continuous in Besov spaces \(B^{s}_{p,r}({\mathbb {T}})\times B^{s}_{p,r}({\mathbb {T}}) \) with \(s>\max \{5/2,2+1/p\}, 1\le p,r\le \infty \) and \(B^{5/2}_{2,1}({\mathbb {T}})\times B^{5/2}_{2,1}({\mathbb {T}})\) through the method of approximate solutions. Furthermore, it is in the non-periodic case that the non-uniform continuity of this solution map in Besov spaces \(B^{s}_{p,r}({\mathbb {R}})\times B^{s}_{p,r}({\mathbb {R}})\) with \(s>\max \{5/2,2+1/p\}, 1\le p,r\le \infty \) is discussed by constructing new subtle initial data. Finally, the Hölder continuity of the solution map in Besov spaces is proved.

这里考虑的是具有峰值的两组分Novikov系统的初值问题。根据该问题的局部适定性结果，表明该问题在周期情况下的解映射\（z_ {0} \ mapsto z（t）\）在Besov空间\（B ^ {S} _ {p，R}（{\ mathbb【T}}）\倍乙^ {S} _ {p，R}（{\ mathbb【T}}）\）与\（S> \最大\ {5 / 2,2 + 1 / p \}，1 \ le p，r \ le \ infty \）和\（B ^ {5/2} _ {2,1}（{\ mathbb {T}} ）通过近似解的方法乘以B ^ {5/2} _ {2,1}（{\ mathbb {T}}）\）。此外，在非周期情况下，此解映射在Besov空间\（B ^ {s} _ {p，r}（{\ mathbb {R}}）\ x B ^ { s} _ {p，r}（{\ mathbb {R}}）\）与通过构造新的细微初始数据来讨论\（s> \ max \ {5 / 2,2 + 1 / p \}，1 \ le p，r \ le \ infty \）。最后，证明了Besov空间中解图的Hölder连续性。