What question did this study set out to answer?

To develop an energy-helicity compensated spectral defect for the Navier-Stokes equations and establish continuation criteria for solutions.

July 20, 2026Open Access

Energy-Helicity Compensated Spectral Depletion for the Three-Dimensional Navier-Stokes Equations with Exact Cone-Mellin Identities

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Preprint introduces spectral defect for Navier-Stokes equations, suggesting criteria for solution continuation.

To develop an energy-helicity compensated spectral defect for the Navier-Stokes equations and establish continuation criteria for solutions.
Introduced K_EH(u) as an energy-helicity compensated spectral defect.
Derived estimates for the nonlinear depletion relating to projective coefficients and moments.
Provided exact representations involving Gram-matrix and Mellin superposition for transport equations.
Key inequality relates nonlinear estimates and spectral defect with exact constants.
Conditions for finiteness of K_EH(u(t))^2 provide a scale-critical continuation criterion.
Demonstrated exact cone-Mellin equations confirming structural balances and limitations in spectral analysis.

David Gutierrez Ule (2026) studied this question.

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