For the purposes of this article, the subject of the kinetic theory of gases is considered to be coextensive with the theory of the Boltzmann equation. We consider only the original equation of… Expand

The precise mathematical relation that the Hilbert and Chapman‐Enskog expansions bear to the manifold of solutions of the Boltzmann equation is described. These expansions yield inherently imprecise… Expand

In Part I the scattering transform method is used to study the weak limit of solutions to the initial value problem for the Korteweg-deVries (KdV) equation as the dispersion tends to zero. In that… Expand

I t is well known that a complete set of orthonormal polynomials in N variables can be obtained by using products of such polynomials in a single variahle. Such a procedure lacks symmetry, and there… Expand

Introduction The physical problem of the propagation of small disturbances (sound waves) corresponds to linearization of the equations in the appropriate mathematical formulation. In an inviscid… Expand

The question of plasma containment in a torus is much more complicated than in an open‐ended mirror system. Serious questions arise of the nonexistence of flux surfaces, of noncontained particle… Expand

It is a classical result for solutions of the Boltzmann equation that Boltzmann’s H-function decreases monotonically with time, but ceases to decrease if the distribution function becomes locally… Expand