Global semigroup of conservative weak solutions of the two-component Novikov equation

We study the Cauchy problem for the two-component Novikov system with initial data u0,v0 in H1(R) such that the product (∂xu0)∂xv0 belongs to L2(R). We construct a global semigroup of conservative weak solutions. We also discuss the potential concentration phenomena of (∂xu)2dx, (∂xv)2dx, and (∂xu)2...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 86; p. 104393
Main Authors Karlsen, K.H., Rybalko, Ya
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2025
Subjects
Cubic nonlinearity
Global well-posedness
Nonlocal (Alice–Bob) integrable system
Novikov equation
Two-component peakon equation
secondary
Novikov equation
Cubic nonlinearity
Global well-posedness
Nonlocal (Alice–Bob) integrable system
Two-component peakon equation
primary
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Summary:We study the Cauchy problem for the two-component Novikov system with initial data u0,v0 in H1(R) such that the product (∂xu0)∂xv0 belongs to L2(R). We construct a global semigroup of conservative weak solutions. We also discuss the potential concentration phenomena of (∂xu)2dx, (∂xv)2dx, and (∂xu)2(∂xv)2dx, which contribute to wave-breaking and may occur for a set of time with nonzero measure. Finally, we establish the continuity of the data-to-solution map in the uniform norm.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2025.104393