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Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces

  • Haokun Tai
  • Xiaoxin Zheng
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Abstract

This paper examines the stability analysis of two-dimensional incompressible fluids in L2uloc spaces. Extending the classical stability framework for Euler equations in Yudovich-type settings, we establish the convergence of Navier-Stokes solutions toward Euler solutions as viscosity ν→ 0, under the weakened assumptions uν0 ∈ L∞ and ων0 ∈ L∞ without imposing decay conditions at infinity. We first derive a priori estimates for the Navier-Stokes equations in L∞ spaces. Then, using harmonic analysis tools including Littlewood-Paley decomposition and Bony's paraproduct calculus, we prove the L∞-convergence of the velocity field and L2uloc-convergence of the vorticity as ν→ 0.

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Cite

BibTeXRIS
BibTeX
@misc{tai2026stability,
  title = {{Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces}},
  author = {Haokun Tai and Xiaoxin Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18102},
  eprint = {2610.18102},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18102},
}
RIS
TY  - UNPB
TI  - Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces
AU  - Haokun Tai
AU  - Xiaoxin Zheng
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18102
UR  - https://arxiv.org/abs/2610.18102
AB  - This paper examines the stability analysis of two-dimensional incompressible fluids in L^2_uloc spaces. Extending the classical stability framework for Euler equations in Yudovich-type settings, we establish the convergence of Navier-Stokes solutions toward Euler solutions as viscosity ν→ 0, under the weakened assumptions u^ν_0 ∈ L^∞ and ω^ν_0 ∈ L^∞ without imposing decay conditions at infinity. We first derive a priori estimates for the Navier-Stokes equations in L^∞ spaces. Then, using harmonic analysis tools including Littlewood-Paley decomposition and Bony's paraproduct calculus, we prove the L^∞-convergence of the velocity field and L^2_uloc-convergence of the vorticity as ν→ 0.
ER  -