Document Type
Article
Publication Date
2026
Keywords
BRST Conserved Moments, Navier-Stokes Solutions, Euler Equation
Abstract
This note adds a missing proof for an assertion in the original paper Gauge Invariance and Repeated Time Isolated Solution Discontinuities.
The assertion is that under weak limits and within a constant energy isosurface, enstrophy is conserved up to losses due to viscous dissipation.
According to the BRST theory for quantum Yang-Mills fields, the conserved moments are exactly those with infinite vacuum expectation values. Application of the BRST theory to fluids is explored. The BRST restriction to the loop expansion (fixed space) is justified by the reqirement that a perturbative expansion can be constructed. In this case the theory predicts exactly three conservation laws for Navier-Stokes incompressible fluids, or only two if the $\pm$ enstrophy orientations are regarded as a single theory. One conservation law was known previously and the other one or two identified here.
The theory predicts the same three or two conservation laws for Ising model fluids, explicitly identified.
A notion of weak convergence with cutoffs order by order for the fluid (Navier-Stokes or Euler) is sketched, with uniformity of the Euler limit as the viscosity $\nu \to 0$.
Recommended Citation
Glimm, James, "BRST Conserved Moments for Fluids" (2026). Department of Applied Mathematics & Statistics Faculty Publications. 9.
https://commons.library.stonybrook.edu/ams-articles/9