00-38 Oliver Knill

An existence theorem for Vlasov gas dynamics in regions with moving boundaries (59K, LATeX 2e) Jan 24, 00

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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.

Files: 00-38.tex