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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14240 |
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| _version_ | 1866911781889245184 |
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| author | Chen, Gui-Qiang G. Glimm, James Said, Hamid |
| author_facet | Chen, Gui-Qiang G. Glimm, James Said, Hamid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Principle of Maximum Entropy for the Navier-Stokes Equations Chen, Gui-Qiang G. Glimm, James Said, Hamid Fluid Dynamics Mathematical Physics Analysis of PDEs Classical Physics 28D20, 76F02, 28C20, 76D05, 49S05, 35A15, 70G10, 35Q30, 37A50 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. |
| title | A Principle of Maximum Entropy for the Navier-Stokes Equations |
| topic | Fluid Dynamics Mathematical Physics Analysis of PDEs Classical Physics 28D20, 76F02, 28C20, 76D05, 49S05, 35A15, 70G10, 35Q30, 37A50 |
| url | https://arxiv.org/abs/2402.14240 |