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

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 via rescaled trajectory functionals, Simon's BV compactness lemma, and balanced-viscosity formulations. Numerical validation on the Lorenz attractor confirms that the dissipation-sublevel sets are precompact (DS3 holds). Published in English and German versions. Part of the Functional Stability Theory (FST) programme.