The cold limit of Navier-Stokes: A peak-vorticity estimate at R13
Year: 2026
Type: preprint
Abstract: On axisymmetric Hou-Luo-type vortex-tube data, this paper derives a peak-vorticity threshold estimate for the Struchtrup-Torrilhon regularized 13-moment (R13) system with temperature-dependent viscosity μ(T) = μ0(T/T0)s, together with a conditional singular-limit statement identifying the incompressible isothermal constant-viscosity Navier-Stokes system as the s = 0 velocity-field degeneration of the R13 mechanism. The threshold estimate. A steady heat balance on the axisymmetric vortex tube, closed by a Kirchhoff transformation of the quasi-linear temperature equation, yields an exact core-temperature lower bound (Appendix A). Its threshold form produces a peak-vorticity scale that, at fixed Reynolds number, diverges as s → 0+ according to Vmax(s) ∼ s Re01/s / log Re0. A Chapman-Enskog upper bound in the joint stress-and-heat-flux regime, together with a Maxwell-surrogate stress-relaxation lower bound at threshold crossing (Appendix B), frames the two-regime behaviour. The profile-comparison condition χs ≥ 1/(2π(s+1)) required for the surrogate transfer to the Hou-Luo meridional profile is verified numerically on the Lamb-Oseen strain-integrand across the tested parameter range (accompanying script chi_s_verification.py: χs ∈ [0.86, 0.97] with 8× to 12× margin). The singular limit. For R13 families reaching the threshold interval on a common finite time window, the paper's conditional statement identifies the s → 0+ velocity limit as a Leray-Hopf weak solution of the constant-viscosity Navier-Stokes system, with the R13 vorticity divergence transferring to the Beale-Kato-Majda continuation obstruction on that limit. The identification depends on joint modulated-energy compactness on the (u, T, Π) system (templated on the Bardos-Golse-Levermore programme), a near-maximum-vorticity duration lower bound, R13-side stress and heat-flux comparison estimates, and a no-concentration lower-semicontinuity transfer. Under the Hou-Luo axisymmetric blow-up conjecture for the target Navier-Stokes system at high Reynolds number, the singular limit reads as a routing of the finite-time-singularity question to the removed R13 damping mechanism (§6.3).
Author: Tan, Daniel Fook Hao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167429384
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