A Thermodynamic Obstruction to Finite-Time Blow-Up in the 3D Navier-Stokes Equations

DRAFT version. This is an advanced conditional preprint and remains subject to revision. It does not claim an unconditional resolution of the 3D Navier-Stokes millennium problem; the exclusion of finite-time blow-up is conditional on the stated BV-selection and dissipation-dominance hypotheses. We propose a thermodynamic obstruction to finite-time blow-up in the 3D Navier–Stokes equations. Using a free-energy functional on the global attractor, we derive a conditional regularity criterion: if a BV-regular selection on the attractor exists (Assumption G) and a dissipation-dominance condition holds (Condition D), then finite-time blow-up is excluded. We introduce an EDP-convergence route to selection regularity…