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PreprintCC BY 4.0arXiv

Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows

  • Yaniv Almog
  • Bernard Helffer
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Abstract

We consider the spectrum of the Orr-Sommerfeld operator, which is obtained from the linearized Navier-Stokes (LNS) operator near a laminar flow in an infinite two-dimensional channel in the large Reynolds number limit. For a rather general class of laminar flows, which behave locally near the boundary like a Couette flow and are bounded from below (above) by a linear increasing (decreasing) function, we show that there exists an eigenvalue of the LNS operator which coincides, to leading order, with the eigenvalue of LNS near Couette flow, which was formally obtained by Wasow in 1953.

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Cite

BibTeXRIS
BibTeX
@misc{almog2026eigenvalues,
  title = {{Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows}},
  author = {Yaniv Almog and Bernard Helffer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12029},
  eprint = {2609.12029},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12029},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Eigenvalues of the linearized Navier-Stokes operator near locally Couette laminar flows
AU  - Yaniv Almog
AU  - Bernard Helffer
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.12029
UR  - https://arxiv.org/abs/2609.12029
AB  - We consider the spectrum of the Orr-Sommerfeld operator, which is obtained from the linearized Navier-Stokes (LNS) operator near a laminar flow in an infinite two-dimensional channel in the large Reynolds number limit. For a rather general class of laminar flows, which behave locally near the boundary like a Couette flow and are bounded from below (above) by a linear increasing (decreasing) function, we show that there exists an eigenvalue of the LNS operator which coincides, to leading order, with the eigenvalue of LNS near Couette flow, which was formally obtained by Wasow in 1953.
ER  -