A Principle of Maximum Entropy for the Navier-Stokes Equations
Copyright policy )A Principle of Maximum Entropy for the Navier-Stokes Equations
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.
Comment: 12 Pages
- Stony Brook University United States
- Kuwait University Kuwait
- Mathematical Institute, University of Oxford United Kingdom
- University of Oxford United Kingdom
energy-enstrophy surface, Navier-Stokes equations for incompressible viscous fluids, 28D20, 76F02, 28C20, 76D05, 49S05, 35A15, 70G10, 35Q30, 37A50, Physics - Fluid Dynamics, Physics - Classical Physics, Dynamical systems and their relations with probability theory and stochastic processes, principle of maximum entropy, Fundamentals of turbulence, Variational methods applied to PDEs, Mathematics - Analysis of PDEs, Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics, Navier-Stokes equations, Variational principles of physics, Mathematical Physics, fully developed turbulence
energy-enstrophy surface, Navier-Stokes equations for incompressible viscous fluids, 28D20, 76F02, 28C20, 76D05, 49S05, 35A15, 70G10, 35Q30, 37A50, Physics - Fluid Dynamics, Physics - Classical Physics, Dynamical systems and their relations with probability theory and stochastic processes, principle of maximum entropy, Fundamentals of turbulence, Variational methods applied to PDEs, Mathematics - Analysis of PDEs, Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics, Navier-Stokes equations, Variational principles of physics, Mathematical Physics, fully developed turbulence
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