Asymptotic Equivalence of the Navier-Stokes and Nonlinear Boltzmann Equations

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. One of the most interesting features of the use of Boltzmann's equation to describe the behavior of a gas is the possibility of a radically different macroscopic description of the gas via the navier-stokes or inviscid Euler Equations. The fact that there is an overlapping range where both theories are believed to be valid on physical grounds suggests the strictly mathematical question of a connection between the theories of the Boltzmann and navier-stokes equations. The relationship is extremely singular, first because the variables used to describe the state of the gas are so dissimilar, and second because the time scales on which the gas evolves are apparently unrelated.