Oliver Knill
An existence theorem for Vlasov gas dynamics
in regions with moving boundaries
(59K, LATeX 2e)
ABSTRACT. We prove a global existence theorem for a class of
deterministic infinite-dimensional Hamiltonian
systems in which a Vlasov gas is coupled to a finite-dimensional
Hamiltonian system. The later is the motion of the rigid and macroscopic
boundary. The boundary motion is due to pressure forces of the gas and
determined by the law of total momentum conservation of the coupled system.
Our existence result shows that if the gas density is initially a smooth
function on the phase space, the boundary moves continuously.
We consider specific examples of such a gas dynamics and
formulate some open mathematical questions for these Hamiltonian systems.