A transformation property of the Boltzmann equation
Abstract
A nonlinear integrodifferential equation, known as the Boltzmann equation, which governs the phase density function of a simple gas in the kinetic theory of gases is examined. A proof for a transformation property of the Boltzmann equation is obtained. In its physical interpretation, the main theorem derived states that if a given process of a gas, as characterized by the phase density function, is compatible with the external force field according to the Boltzmann equation, then the process which is a result of superposing a rigid motion on the given process as characterized by a certain Euclidean transformation is compatible with the apparent external force field of the original force field. An expression relating these two fields is derived. Using th transformation property obtained, it is shown that the expression relating the force fields is the governing equation of the phase density function.
 Publication:

Quarterly of Applied Mathematics
 Pub Date:
 January 1976
 Bibcode:
 1976QApMa..33..369W
 Keywords:

 Boltzmann Transport Equation;
 Collision Parameters;
 Gas Dynamics;
 Integral Transformations;
 MaxwellBoltzmann Density Function;
 Vapor Phases;
 Kinetic Theory;
 Molecular Collisions;
 Molecular Gases;
 Stream Functions (Fluids);
 Transformations (Mathematics);
 Fluid Mechanics and Heat Transfer