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Euler and Navier-Stokes limits of the Uehling-Uhlenbeck quantum kinetic equations. (English) Zbl 0885.35102

Summary: The Uehling-Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier-Stokes system are proved.

MSC:

35Q40 PDEs in connection with quantum mechanics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
35Q30 Navier-Stokes equations
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