An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation
| dc.creator | Bressan, Alberto | |
| dc.creator | Fonte, Massimo | |
| dc.date | 2005-04-22 | |
| dc.date | 2005-05-04 | |
| dc.date.accessioned | 2026-07-07T05:19:20Z | |
| dc.date.available | 2026-07-07T05:19:20Z | |
| dc.description | In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space $H^1$. Our solutions are conservative, in the sense that the total energy $\int (u^2+u_x^2) dx$ remains a.e. constant in time. Our new approach is based on a distance functional $J(u,v)$, defined in terms of an optimal transportation problem, which satisfies ${d\over dt} J(u(t), v(t))\leq κ\cdot J(u(t),v(t))$ for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result. | |
| dc.description | 29 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0504450 | |
| dc.identifier | http://arxiv.org/abs/math/0504450 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74985 | |
| dc.subject | Analysis of PDEs | |
| dc.title | An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation | |
| dc.type | text |