A Proof Approach to the Global Regularity of the Navier–Stokes Equations

This paper presents a heuristic approach to the global existence and smoothness problem for the Navier–Stokes equations in three dimensions. Using an analytical framework based on energy estimates and functional inequalities, we explore conditions under which weak solutions remain smooth for all time. The argument draws on intuition from partial differential equations and fluid dynamics, aiming to contribute toward a potential resolution of this Clay Millennium Problem.