PreprintarXiv licencearXiv
Energy conservation of weak solutions and Onsager's conjecture for the two-component Camassa-Holm system
Abstract
In this paper, we investigate energy conservation for weak solutions to the two-component Camassa-Holm system. We derive a local energy balance equation in the sense of distributions with an explicit defect term. As an application, we determine that the Onsager exponent is 1, and as a consequence, we also obtain the uniqueness of weak solutions.
Related
- A Riemann-Hilbert approach to the two-component modified Camassa-Holm system with step-like boundary conditions
- Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field
- Onsager's Conjecture for Ideal Magnetohydrodynamics
- Diffusion stabilises time-periodic solutions in conservation laws coupled to a relaxation oscillator
- Generic Structural Stability for Riemann Solutions to n × n Systems of Hyperbolic Conservation Laws
BibTeX
@misc{liu2026energy,
title = {{Energy conservation of weak solutions and Onsager's conjecture for the two-component Camassa-Holm system}},
author = {Jingjing Liu and Zhaoyu Sun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28034},
eprint = {2609.28034},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28034},
}
RIS
TY - UNPB
TI - Energy conservation of weak solutions and Onsager's conjecture for the two-component Camassa-Holm system
AU - Jingjing Liu
AU - Zhaoyu Sun
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28034
UR - https://arxiv.org/abs/2609.28034
AB - In this paper, we investigate energy conservation for weak solutions to the two-component Camassa-Holm system. We derive a local energy balance equation in the sense of distributions with an explicit defect term. As an application, we determine that the Onsager exponent is 1, and as a consequence, we also obtain the uniqueness of weak solutions.
ER -