A continuous interpolation between conservative and dissipative solutions
Peer reviewed, Journal article
Published version
![Thumbnail](/ntnu-xmlui/bitstream/handle/11250/2652981/Grunert.pdf.jpg?sequence=6&isAllowed=y)
View/ Open
Date
2015Metadata
Show full item recordCollections
- Institutt for matematiske fag [2438]
- Publikasjoner fra CRIStin - NTNU [38041]
Abstract
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.