IndisputableMonolith.NavierStokes.RM2U.Core
The RM2U.Core module defines the tail-flux boundary term B(r) for radial integration-by-parts identities in Navier-Stokes ancient solutions. Researchers on RM2 closure and Bet1 integrability cite this definition to reduce vanishing at infinity to concrete integrability obligations. It is a pure definition module with no internal proofs.
claimThe boundary term is defined by $B(r) := -A(r) · (A'(r) r^2)$, which appears in the radial integration-by-parts identity and matches the zero-skew-at-infinity condition from SkewHarmGate.Radial.
background
In the RM2U analysis of Navier-Stokes ancient elements, radial profiles A(r) are integrated by parts to isolate tail fluxes at infinity. The module introduces the boundary term B(r) to convert vanishing statements into two integrability requirements on the term and its derivative. This construction directly references the SkewHarmGate.Radial.zeroSkewAtInfinity_of_integrable lemma.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The boundary term supplies the algebraic spine for the EnergyIdentity module and enables BetInstantiation of the integrability route for concrete ancient solutions. It supports RM2Closure by preparing the log-critical shell moment finiteness step and feeds TailFluxInstantiation via Galerkin extraction. The definition closes the first link in the RM2U to RM2 pipeline.
scope and limits
- Does not prove vanishing of the tail flux at infinity.
- Does not state or discharge any integrability hypotheses.
- Does not derive coercive L2 bounds or log-critical moment finiteness.
- Does not formulate or address the non-parasitism condition.