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arXiv · 1902.01985

Charles Bouton and the Navier-Stokes Global Regularity Conjecture

J. G. Polihronov
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Abstract

This article examines the Bouton-Lie group invariants of the Navier-Stokes equation (NSE) for incompressible fluids. Bouton's theory is applied to the general scaling transformation admitted by the NSE and is used to derive all self-similar solutions. In light of these, the criticality of the standard NSE system is examined and criticality criteria are derived. The theorem of Beale-Kato-Majda is used to rule out blow-up for a subset of Bouton's self-similar solutions. For a subset of Leray's self-similar solutions, the cavitation number of the fluid is found to be a scale-invariant, conserved quantity. By extending the analysis of Bouton to higher-dimensioned manifolds, additional conserved quantities are found, which could further elucidate the physics of fluid turbulence.

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J. G. Polihronov. 2022-06-02. Charles Bouton and the Navier-Stokes Global Regularity Conjecture. https://doi.org/10.1063/5.0101855

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