Sequences of suitable weak solutions of the Landau-Fermi-Dirac equation converge, up to subsequence, to Villani renormalized solutions of the classical Landau equation in the vanishing quantum parameter limit.
Global solutions to the Landau-Fermi-Dirac equation
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We establish a compactness result for solutions of a certain class of hypoelliptic equations. This result allows us to show the existence of global weak solutions to the non-homogeneous Landau-Fermi-Dirac equation with Coulomb potential.
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On the semi-classical limit for the Landau-Fermi-Dirac equation
Sequences of suitable weak solutions of the Landau-Fermi-Dirac equation converge, up to subsequence, to Villani renormalized solutions of the classical Landau equation in the vanishing quantum parameter limit.