PreprintCC0arXiv
Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality
Abstract
To date, a Leray's weak solution to the Navier-Stokes equations enjoys an energy inequality. We prove the existence of a weak solution that enjoys the energy equality. The existence of the weak solution is achieved as limit of solutions to the mollified Navier-Stokes system (Leray's approach). Since no uniqueness result is known for weak solutions we are not able to claim that any weak solution in the sense of Leray-Hopf enjoys the energy equality.
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BibTeX
@misc{maremonti2026existence,
title = {{Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality}},
author = {Paolo Maremonti and Alfonsina Tartaglione},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35517},
eprint = {2610.35517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35517},
note = {CC0},
}
RIS
TY - UNPB
TI - Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality
AU - Paolo Maremonti
AU - Alfonsina Tartaglione
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35517
UR - https://arxiv.org/abs/2610.35517
AB - To date, a Leray's weak solution to the Navier-Stokes equations enjoys an energy inequality. We prove the existence of a weak solution that enjoys the energy equality. The existence of the weak solution is achieved as limit of solutions to the mollified Navier-Stokes system (Leray's approach). Since no uniqueness result is known for weak solutions we are not able to claim that any weak solution in the sense of Leray-Hopf enjoys the energy equality.
ER -