ArXiv · 2026
This paper provides a rigorous mathematical analysis of the global regularity problem for the 3D incompressible Navier-Stokes (NS) equations, specifically addressing the conditions under which smooth initial data may lead to a loss of regularity. By departing from traditional phenomenological turbulence models and focusing strictly on the mechanical energy transport equation, we derive a fundamental critical condition, u·∇ E = 0, where E = 1/2|u|² + p is the specific mechanical energy, which characterizes the transition from laminar to turbulent flow.
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