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Higher Order Unbounded Rough Drivers
Abstract
We construct a framework for higher order unbounded rough drivers defined by rough paths over vector fields. This allows us to consider a purely Eulerian perspective for rough transport equations where the driving rough path vector field is allowed to have temporal p-variation for any p ∈ (1,∞). We use this framework to show the well-posedness of an equation with two transport terms; one driven by a rough path vector field with aforementioned p-variation in time, and the other driven by a DiPerna--Lions-type drift vector field.
Related
- Higher-Order Paracontrolled Calculus for Geometric Rough Paths
- Rough log-log blowup solutions to mass-critical NLS in higher dimensions d≥ 3
- Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms
- Lp-regularity for fourth-order Schrödinger operators with unbounded or degenerate coefficients
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BibTeX
@misc{nilssen2026higher,
title = {{Higher Order Unbounded Rough Drivers}},
author = {Torstein Nilssen and Jonas Pedersen Vean},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05353},
eprint = {2609.05353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05353},
}
RIS
TY - UNPB
TI - Higher Order Unbounded Rough Drivers
AU - Torstein Nilssen
AU - Jonas Pedersen Vean
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05353
UR - https://arxiv.org/abs/2609.05353
AB - We construct a framework for higher order unbounded rough drivers defined by rough paths over vector fields. This allows us to consider a purely Eulerian perspective for rough transport equations where the driving rough path vector field is allowed to have temporal p-variation for any p ∈ (1,∞). We use this framework to show the well-posedness of an equation with two transport terms; one driven by a rough path vector field with aforementioned p-variation in time, and the other driven by a DiPerna--Lions-type drift vector field.
ER -