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PreprintCC BY 4.0arXiv

Global-in-time inviscid limit of the Navier-Stokes equations for vortex-wave data

  • Trinh T. Nguyen
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Abstract

We justify the vortex-wave system introduced by Marchioro and Pulvirenti in the 1990s as the vanishing-viscosity limit of the two-dimensional Navier-Stokes equations on every prescribed finite time interval. The initial vorticity consists of a point vortex and a smooth, compactly supported background that vanishes near the vortex. The regular component converges strongly to the background vorticity governed by the vortex-wave system, while the concentrated component is approximated by a Lamb-Oseen vortex centered on the limiting point-vortex trajectory. We obtain quantitative estimates for both components, with constants and a viscosity threshold depending on the chosen time interval, thereby providing a global-in-time justification of the vortex-wave system for this class of initial data.

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Cite

BibTeXRIS
BibTeX
@misc{nguyen2026globalintime,
  title = {{Global-in-time inviscid limit of the Navier-Stokes equations for vortex-wave data}},
  author = {Trinh T. Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32233},
  eprint = {2609.32233},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32233},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global-in-time inviscid limit of the Navier-Stokes equations for vortex-wave data
AU  - Trinh T. Nguyen
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32233
UR  - https://arxiv.org/abs/2609.32233
AB  - We justify the vortex-wave system introduced by Marchioro and Pulvirenti in the 1990s as the vanishing-viscosity limit of the two-dimensional Navier-Stokes equations on every prescribed finite time interval. The initial vorticity consists of a point vortex and a smooth, compactly supported background that vanishes near the vortex. The regular component converges strongly to the background vorticity governed by the vortex-wave system, while the concentrated component is approximated by a Lamb-Oseen vortex centered on the limiting point-vortex trajectory. We obtain quantitative estimates for both components, with constants and a viscosity threshold depending on the chosen time interval, thereby providing a global-in-time justification of the vortex-wave system for this class of initial data.
ER  -