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Uniqueness of solutions to the 2D compressible Navier-Stokes equations for bounded densities
Abstract
We prove the uniqueness of global solutions to the two dimensional barotropic compressible Navier--Stokes equations within the regularity class introduced by Danchin and Mucha [14], for general C1 pressure laws. A crucial assumption is that both solutions have bounded divergence, locally integrable in time, which ensures that their densities remain bounded without excluding vacuum or requiring spatial regularity of the density.
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BibTeX
@misc{pescatore2026uniqueness,
title = {{Uniqueness of solutions to the 2D compressible Navier-Stokes equations for bounded densities}},
author = {Lorenzo Pescatore and Alessandro Violini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18178},
eprint = {2610.18178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18178},
}
RIS
TY - UNPB
TI - Uniqueness of solutions to the 2D compressible Navier-Stokes equations for bounded densities
AU - Lorenzo Pescatore
AU - Alessandro Violini
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18178
UR - https://arxiv.org/abs/2610.18178
AB - We prove the uniqueness of global solutions to the two dimensional barotropic compressible Navier--Stokes equations within the regularity class introduced by Danchin and Mucha [14], for general C^1 pressure laws. A crucial assumption is that both solutions have bounded divergence, locally integrable in time, which ensures that their densities remain bounded without excluding vacuum or requiring spatial regularity of the density.
ER -