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Equivalence of Boltzmann and moment equations
Cubarsí Morera, Rafael
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. GAGE - Grup d´Astronomia i Geomatica
The closure problem for the stellar hydrodynamic equations is studied by describing the family of phase space density functions, for which the collisionless Boltzmann equation is strictly equivalent to a finite subset of moment equations. It is proven that the redundancy of the higher-order moment equations and the recurrence of the velocity moments are of similar nature. The method is based on the use of maximum entropy distributions, which are afterwards generalised to phase space density functions depending on any isolating integral of motion in terms of a polynomial function of degree n in the velocities. The equivalence between the moment equations up to an order n + 1 and the collisionless Boltzmann equation is proven. It is then possible to associate the complexity of a stellar system, i.e., the minimum set of velocity moments needed to describe its main kinematic features, with the number of moment equations required to model it.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Kinematics
Hydrodynamics
Galaxies
Statistics
Cinemàtica
Hidrodinàmica
Galàxies
Estadística
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