A Principle of Maximum Entropy for the NavierStokes Equations
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 $L^2$ divergencefree velocity fields, is maximized relative to alternate measures supported over the energyenstrophy surface. Since thermodynamic equilibrium distributions are characterized by maximum entropy, connections are drawn with stationary statistical solutions of the incompressible NavierStokes equations. Special emphasis is on the correspondence with the final statistics described by Kolmogorov's theory of fully developed turbulence.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.14240
 arXiv:
 arXiv:2402.14240
 Bibcode:
 2024arXiv240214240C
 Keywords:

 Physics  Fluid Dynamics;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Physics  Classical Physics;
 28D20;
 76F02;
 28C20;
 76D05;
 49S05;
 35A15;
 70G10;
 35Q30;
 37A50
 EPrint:
 12 Pages