Solution of the Regularity of the Navier-Stokes Equations

Solution au probleme de la régularité des equations Navier Stokes_Complet_FR1.pdf

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Solution to the Regularity Problem of the Navier-Stokes Equations_ANG1.pdf

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This work presents an innovative probabilistic approach to solving the regularity problem of incompressible Navier-Stokes equations in 3D, by reformulating fluid dynamics via a multi-scale state function P(t). The modeling relies on P(t) = A ψ(S, R, V, D[D_cond, D_act], C, T, M) ⋅ [O(t) ⋅ D(t)], integrating multi-scale interactions, instabilities, and energy dissipation, with a dynamic memory M to stabilize turbulence. Analytical derivations prove equivalence to the Navier-Stokes equations and establish global bounds for solution regularity, validated by theoretical analyses and numerical simulations.