Non-uniqueness of integral curves for autonomous Hamiltonian vector fields
Analysis of PDEs
2021-08-12 v1
Abstract
In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport equation has non-unique positive solutions. As a consequence of Ambrosio superposition principle, we show that this vector field has non-unique integral curves with a positive Lebesgue measure set of initial data and moreover we show that the Hamiltonian is not constant along these integral curves.
Keywords
Cite
@article{arxiv.2108.05050,
title = {Non-uniqueness of integral curves for autonomous Hamiltonian vector fields},
author = {Vikram Giri and Massimo Sorella},
journal= {arXiv preprint arXiv:2108.05050},
year = {2021}
}
Comments
15 pages