Problems Connected with the Boltzmann Equation

What are the mathematical properties of the nonlinear Boltzmann equation  

In particular, for what class of intermolecular potentials does this equation have a unique solution for given initial and boundary conditions Is the normal solution of Chapman and Enskog in any sense a good approximation to the actual solution, at least sufficiently far from the boundaries, and for sufficiently long times Can one find explicit solutions to the nonlinear Boltzmann equation with sufficient accuracy so that the specifically nonlinear features of the Boltzmann equation can be tested, in shock wave or sound wave or sound propagation experiments, for example  

What are the general features of the approach to equilibrium of a gas when there are boundaries present  

In this connection it is worth pointing out that for the Kramers problem, an exact solution to the linearized Boltzmann equation for a BGK model gas has been constructed by Cercignani. Even for this case the answers to questions (a) and (b) are not known.  

For the case of a gas flow around a simple convex object such as a sphere or cylinder, where characterizes the size of the object, some progress has been made on this problem by demonstrating the relation between the various microscopic processes that are important in each region. The 

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