The simplest system in Levermore's moment hierarchy involving moments higher than second order is the five-moment closure. It is obtained by taking velocity moments of the one-dimensional Boltzmann equation under the assumption that the velocity distribution is a maximum-entropy function. The moment vectors for which a maximum-entropy function exists consequently make up the domain of definition of the system. The aim of this article is a complete characterization of the structure of the domain of definition and the connected maximum-entropy problem. The space-homogeneous case of the equation and numerical aspects are also addressed.
Levermore's moment closuremaximum entropymoment realizabilityreduced Hamburger moment problem