Global semigroup of conservative weak solutions of the two-component Novikov equation - Karlsen, K.H.; Rybalko, Ya (Nonlinear analysis: real world applications, 2025)
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.