The Principle of Yin-Yang Mutual Restriction for the Global Regularity of the 3D Navier–Stokes Equations: A Reexamination from an Eastern Perspective

The existence of global smooth solutions to the 3D incompressible Navier–Stokes equations is one of the famous Millennium Prize Problems in mathematics. To date, the mathematical community has not found effective a priori estimates to control the vorticity stretching mechanism, and thus cannot rule out the possibility of finite-time blowup. This is a conceptual framework paper, not a final mathematical proof. Based on the core ideas of Tai Chi Yin-Yang—mutual generation and mutual constraint, conservation and balance, Yin within Yang, and Yang within Yin—this paper proposes a principle of Yin-Yang mutual restriction to explain the inherent stability of fluid systems, and identifies the central difficulty in traditional proofs: the lack of mathematical tools that describe the mutual inhibition of coupled physical quantities and prevent their independent unbounded growth. This paper strictly distinguishes known facts from conjectures, clarifies its academic scope, and proposes a weak axiomatic approach consistent with mainstream research. It offers an Eastern holistic perspective for understanding the Navier–Stokes equations, with both heuristic and progressive academic value.