A sufficiency class for global (in time) solutions to the 3D Navier–Stokes equations

Let Ω be an open domain of class C 2 contained in R 3 , let L 2 ( Ω ) 3 be the Hilbert space of square integrable functions on Ω and let H [ Ω ] ≔ H be the completion of the set, { u ∈ ( C 0 ∞ [ Ω ] ) 3 ∣ ∇ ⋅ u = 0 } , with respect to the inner product of L 2 ( Ω ) 3 . A well-known unsolved problem...

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