PreprintCC BY 4.0arXiv
The inviscid limit of 2D Navier-Stokes near a self-similar vortex collapse
Abstract
We study the inviscid limit of the two-dimensional Navier--Stokes equations with initial vorticity given by three point vortices whose inviscid trajectories collapse self-similarly at t=1. For every fixed 0<γ<1, we prove that the solution is approximated by a superposition of Lamb--Oseen vortices centered at the point-vortex positions, with an L1 error of order O(ν1−γ), uniformly for 0<t≤ Tν=1−νγ. We use coordinates adapted to the self-similar collapse and study a long-time inviscid limit problem on the interval 0<s≤γlog(1/ν), with a time-dependent rescaled diffusion coefficient η(s) that tends to zero as s→∞.
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BibTeX
@misc{nguyen2026inviscid,
title = {{The inviscid limit of 2D Navier-Stokes near a self-similar vortex collapse}},
author = {Trinh T. Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25367},
eprint = {2610.25367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25367},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The inviscid limit of 2D Navier-Stokes near a self-similar vortex collapse
AU - Trinh T. Nguyen
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25367
UR - https://arxiv.org/abs/2610.25367
AB - We study the inviscid limit of the two-dimensional Navier--Stokes equations with initial vorticity given by three point vortices whose inviscid trajectories collapse self-similarly at t=1. For every fixed 0<γ<1, we prove that the solution is approximated by a superposition of Lamb--Oseen vortices centered at the point-vortex positions, with an L^1 error of order O(ν^1−γ), uniformly for 0<t≤ T_ν=1−ν^γ. We use coordinates adapted to the self-similar collapse and study a long-time inviscid limit problem on the interval 0<s≤γlog(1/ν), with a time-dependent rescaled diffusion coefficient η(s) that tends to zero as s→∞.
ER -