A continuous interpolation between conservative and dissipative solutions
Peer reviewed, Journal article
Published version
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https://hdl.handle.net/11250/2652981Utgivelsesdato
2015Metadata
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- Institutt for matematiske fag [2533]
- Publikasjoner fra CRIStin - NTNU [38576]
Sammendrag
We introduce a novel solution concept, denoted -dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line with vanishing asymptotics. All the -dissipative solutions are global weak solutions of the same equation in Eulerian coordinates, yet they exhibit rather distinct behavior at wave breaking. The solutions are constructed after a transformation into Lagrangian variables, where the solution is carefully modified at wave breaking.