Do the two singular limits commute — c → ∞ and ν → 0?

Status: open · laid 2026-09-13 · type: derivation

Statement. The "two faces" idea was resolved: pressure nonlocality and dissipation are the same angular projector at different points on the Mellin line, and the Leray projection is what bulk viscosity becomes when the radial degree drops from 2 to 0 in the infinite-sound-speed limit. What that resolution generated is open. c → ∞ and ν → 0 act on different sectors. Onsager's anomalous dissipation is a transverse-sector statement about ν → 0 at fixed c = ∞.

Friction. Approaching the Euler singularity along a path with c large but finite may behave differently from approaching it at c = ∞ first — and if it does, finite sound speed is a more natural regularization of NS than hyperviscosity, since it keeps both faces at degree 2 with nothing nonlocal to fight. Nothing yet says whether the order of the two limits matters.

Question. Do the two singular limits commute? If not, which order is the one Onsager's statement lives in, and does finite sound speed regularize the transverse sector in a way hyperviscosity does not? A satisfactory answer states the two iterated limits and either shows them equal or exhibits the sector where they differ.

Relation to CASE-07 (closures don't commute): undetermined. This has the shape of CASE-07 in a new subject. Whether it is the same non-commutation — one theorem, two instances — or only the same shape is the mechanism test, and the results should decide it, not a call made at filing time. The relation: field stays undetermined until they do.