Boltzmann Equation: Global Existence for a Rare Gas in an Infinite Vacuum

摘要

It is proved that the Boltzmann equation has a unique solution, global in time, in all space. The conditions are: (1) that the initial data go to zero fast enough at infinity, and (2) that the mean free path is large enough. In the case of a finite volume of gas released into a infinite vacuum, results show that the corresponding solution of the Boltzmann equation exists globally if the gas is rare enough. The paradigm shows that infinity should be absorbing, and so it is. Under conditions (1) and (2), it is proved that all molecules are eventually swept out of any finite domain. Thus equilibrium is always trivial.