mathematical physics

We reduce the global regularity problem for the three-dimensional incompressible Navier-Stokes equations to a single quantitative estimate: the integrability of the adiabatic error in the Gallay-Wayne convergence of vortex cross-sections to the Burgers profile.

We present a machine-verified proof framework for the global regularity of the three-dimensional incompressible Navier-Stokes equations, reduced to exactly 18 theorems. The logical chain — from six standard inputs through a contradiction argument — is verified by an automated proof kernel with zero failures.

We prove global existence and smoothness of solutions to the three-dimensional incompressible Navier-Stokes equations for arbitrary smooth, divergence-free initial data with finite energy.