PreprintCC BY 4.0arXiv
The Inviscid Limit in Uniformly Local Yudovich Spaces
Abstract
We consider solutions to the two-dimensional Navier-Stokes and Euler equations with the velocity in L∞(ℝ2) and the vorticity in the uniformly local Yudovich space Yθul(ℝ2). We show that if θ grows sufficiently slowly, then for every T>0, solutions of the Navier-Stokes equation converge to solutions of the Euler equation in L∞([0,T];L2ul(ℝ2)) as ν→ 0+, provided they are generated from the same initial data.
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BibTeX
@misc{radke2026inviscid,
title = {{The Inviscid Limit in Uniformly Local Yudovich Spaces}},
author = {Zachary Radke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13898},
eprint = {2610.13898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13898},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Inviscid Limit in Uniformly Local Yudovich Spaces
AU - Zachary Radke
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13898
UR - https://arxiv.org/abs/2610.13898
AB - We consider solutions to the two-dimensional Navier-Stokes and Euler equations with the velocity in L^∞(ℝ^2) and the vorticity in the uniformly local Yudovich space Y^θ_ul(ℝ^2). We show that if θ grows sufficiently slowly, then for every T>0, solutions of the Navier-Stokes equation converge to solutions of the Euler equation in L^∞([0,T];L^2_ul(ℝ^2)) as ν→ 0^+, provided they are generated from the same initial data.
ER -