About the use of entropy production for the Landau-Fermi-Dirac equation. (English) Zbl 1466.76054
Summary: In this paper, we present new estimates for the entropy dissipation of the Landau-Fermi-Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.
MSC:
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 76P99 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
| 82D05 | Statistical mechanics of gases |
| 82D15 | Statistical mechanics of liquids |
Keywords:
soft potential; Landau equation; quantum kinetic modes; entropy; Fisher information; regularity; long-time behaviourReferences:
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