l've developed a geometric stability analysis for potential Navier-Stokes singularities using the Widnall instability of vortex filaments.
Key results:
• Strong Type I blow-up (C_blow > 0.77) geometrically impossible: physical perturbation &(t)
diverges before T*
• All double-log Type II/III profiles eliminated via double-exponential precession dominance
Weak Corridor (C_blow ≤ 0.77) + axisymmetry
remain open problems
Core math:
For Leray self-similar profiles R(t) ~ C_blow/(T*-t),
relative roughness n(t) = (T*-t) ^(-v_W C_blow)
Physical amplitude a(t) = n(t)•a(t) = (T*-t) ^ (1/2 – v_W
C_blow) → ∞ when C_blow > 1/(2y_W) = 0.77
(Y_W = 0.65 from Widnall 1974 most unstable m=2
mode)
Novel contribution: First quantitative threshold
For Leray self-similar profiles R(t) ~ C_blow/(T*-t),
relative roughness n(t) = (T*-t) ^(-v_W C_blow)
Physical amplitude a(t) = n(t)•a(t) = (T*-t) ^ (1/2 – v_W
C_blow) → ∞ when C_blow > 1/(2y_W) = 0.77
(Y_W = 0.65 from Widnall 1974 most unstable m=2
mode)
Novel contribution: First quantitative threshold
by RonaldPittmanjr
4 Comments
You might want to give some explanation on what you are testing before dumping calculations on us.
Does this even belong on this sub? I’m seeing math (too tired to analyze it right now), and the Navier–Stokes equations are about fluid mechanics, but I’m not seeing any Alternative History.
I recognize this! It’s the diagram from that one scroll that burned at Alexandria- he’s returning the lost knowledge to our blessed sub!!
Why are you posting this in a sub about alternative history where you KNOW most people don’t have the ability to challenge your claims directly?
If this is a novel contribution to the field of mathematics, why aren’t you going through the appropriate channels?