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

• Published in: Nonlinear analysis: real world applications Vol. 86; p. 104393
• Main Authors: Karlsen, K.H., Rybalko, Ya
• Format: Journal Article
• Language: English
• 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

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...