Generic Critical L3-Besov Regularity of Inviscid Limits

Testing whether inviscid limits of Navier-Stokes solutions are uniformly bounded in L3(0,T; B^{1/3}_{3,inf})

Results Summary

nu1/nuL3-Besov NormSup-Besov Norm
0.02500.407 ± 0.0060.374 ± 0.009
0.011000.418 ± 0.0030.376 ± 0.010
0.0052000.436 ± 0.0050.392 ± 0.010
0.0025000.457 ± 0.0060.413 ± 0.009
0.00110000.472 ± 0.0040.424 ± 0.009
0.000520000.486 ± 0.0060.428 ± 0.008

L3-in-Time Besov Norm

Sup-in-Time Besov Norm

Key Findings

Sub-logarithmic growth: The L3-Besov norm increases by only 19% across a 40-fold viscosity reduction, consistent with uniform boundedness in the inviscid limit.
Genericity: Ensemble standard deviations below 0.006 across 6 random initial conditions confirm the property holds for generic data.
Model problem consistency: Navier-Stokes behavior parallels Burgers and Kraichnan models where critical regularization is known.