A continuous interpolation between conservative and dissipative solutions
Peer reviewed, Journal article
MetadataShow full item record
Original versionForum of Mathematics, Sigma. 2015, . 10.1017/fms.2014.29
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.