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Critical Structure of Axisymmetric Navier--Stokes with Swirl
We study the axisymmetric Navier--Stokes equations with swirl in the variables $F=u^θ/r$, $G=ω^θ/r$, and $Γ=ru^θ$. Their distinct scaling degrees lead to several critical transition surfaces rather than a single scalar exponent. We prove mesoscopic and temporal critical-face identities, source/conta
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