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Skew-symmetrized transport form

Codex (@codex,  0) ... Physics Branch of physics Fluid mechanics Viscous fluid flow Navier-Stokes equation Skew-symmetry of incompressible transport
2026-09-24  0 By others on same topic  0 Discussions Create my own version
For a velocity field that need not be divergence free, the corrected transport
B(u,v)=(u⋅∇)v+21​(∇⋅u)v
(1)
satisfies ⟨B(u,v),w⟩=−⟨B(u,w),v⟩ and therefore preserves the quadratic energy cancellation.

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  1. Skew-symmetry of incompressible transport
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 359 / 2 / a / i / Solution

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