A Principle of Maximum Entropy for the Navier-Stokes Equations

Gui-Qiang G. Chen; James Glimm; Hamid Said

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arXiv · 2402.14240

A Principle of Maximum Entropy for the Navier-Stokes Equations

Gui-Qiang G. Chen·James Glimm·Hamid Said

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Abstract

A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to alternate measures supported over the energy--enstrophy surface. Since thermodynamic equilibrium distributions are characterized by maximum entropy, connections are drawn with stationary statistical solutions of the incompressible Navier-Stokes equations. Special emphasis is on the correspondence with the final statistics described by Kolmogorov's theory of fully developed turbulence.

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Gui-Qiang G. Chen, James Glimm, Hamid Said. 2024-02-22. A Principle of Maximum Entropy for the Navier-Stokes Equations. https://arxiv.org/abs/2402.14240

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