A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system
Analysis of PDEs
2022-01-17 v1
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.
Cite
@article{arxiv.1402.1060,
title = {A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system},
author = {Katrin Grunert and Helge Holden and Xavier Raynaud},
journal= {arXiv preprint arXiv:1402.1060},
year = {2022}
}
Comments
58 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1301.1445