Maximum Entropy Moment Problems and Extended Euler Equations
The reduction of kinetic equations to moment systems leads to a closure problem because material laws have to be expressed in terms of the moment variables. In the maximum entropy approach, the closure problem is solved by assuming that the kinetic distribution function maximizes the entropy under some constraints. For the case of Boltzmann equation, the resulting hyperbolic moment systems are investigated. It turns out that the systems generally have non-convex domains of definition. Moreover, the equilibrium state is typically located on the boundary of the domain of definition where the fluxes are singular. This leads to the strange property that arbitrarily close to equilibrium the characteristic velocities of the moment system can be arbitrarily large.
Key wordsmaximum entropy moment methods moment realizability
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