The proposed action does not demonstrably produce the Navier-Stokes equations; the velocity variation is algebraic and the gauge-field equation is only a static Helmholtz equation.
Witten, Quantum field theory and the Jones polynomial ,Communications in Mathematical Physics, 121,351,1989
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A Gauge-Theoretic Action Principle for Viscous Incompressible Fluids
The proposed action does not demonstrably produce the Navier-Stokes equations; the velocity variation is algebraic and the gauge-field equation is only a static Helmholtz equation.