Globally hyperbolic moment model of arbitrary order for three-dimensional special relativistic Boltzmann equation
This work provides a mathematically rigorous framework for moment models of the relativistic Boltzmann equation, which is important for researchers in kinetic theory and relativistic fluid dynamics.
The authors extend a model reduction method to the 3D special relativistic Boltzmann equation, deriving arbitrary-order moment systems that are globally hyperbolic and linearly stable. They provide recurrence relations and derivatives for the required orthogonal polynomials and real spherical harmonics.
This paper extends the model reduction method by the operator projection to the three-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order moment system is built on our careful study of infinite families of the complicate Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics. We derive the recurrence relations of the polynomials, calculate their derivatives with respect to the independent variable and parameter respectively, and study their zeros. The recurrence relations and partial derivatives of the real spherical harmonics are also given. It is proved that our moment system is globally hyperbolic, and linearly stable. Moreover, the Lorentz covariance is also studied in the 1D space.