Constitutive relations in the kinetic theory of gases

Thermomechanical theories of gases fall into two general categories, one consisting of the kinetic theory of gases, the other encompassing continuum theories of fluids. One of the basic ingredients of theories of the latter type is the specification of constitutive relations, these being equations which define the stress and heat flux as functions of the fields of density, velocity, and temperature. They contain the appropriate information about the type of gas being modeled. In contrast to this, the kinetic theory describes a gas through a molecular density function F, and a fundamental axiom in the theory is the requirement that this function satisfy the Maxwell-Boltzmann equation, an integro-differential equation which contains the relevant information about the gas as described by the properties of its molecules. The question of whether constitutive relations are present in the kinetic theory is discussed.