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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 12
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Research Article

On the Cauchy problem for the two-component Novikov system with peakons

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Pages 3418-3443 | Received 10 Feb 2022, Accepted 07 Apr 2022, Published online: 28 Apr 2022
 

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 z0z(t) of this problem on the line is not uniformly continuous in Besov spaces (B2,rs(R))2 with s>3/2,2r through the method of approximate solutions. Next, in the periodic case, the non-uniform continuity of the solution map in Besov spaces (Bp,rs(T))2 and Hölder spaces (Cq(T))2 with s>max{3/2,1+1/p},q>3/2,qR+N,1p,r is discussed. Finally, the Hölder continuity of this solution map in Sobolev spaces is investigated.

MSC (2020):

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundamental Research Program of Shanxi Province [Program No. 20210302124259].

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