Uniform Coulomb-case estimates in the quantum parameter

Determine whether regularity estimates for the spatially homogeneous Landau–Fermi–Dirac equation with Coulomb interactions can be made uniform in the quantum parameter.

Background

The paper reviews prior results for the spatially homogeneous Landau–Fermi–Dirac equation and emphasizes that the Coulomb case is substantially different from hard and moderately soft potentials. Although global existence is known in the homogeneous Coulomb setting, the dependence of regularity estimates on the quantum parameter remains unresolved. Uniform estimates would be important for understanding the semiclassical limit and the relationship between the quantum and classical Landau equations.

References

In particular, it remains largely open whether regularity estimates can be made uniform in $$ in the Coulomb case, and whether LFD admits a monotone Fisher information functional analogous to that of the classical equation.

— Global smooth solutions to the inhomogeneous Landau-Fermi-Dirac equation  (2608.31071 - Golding et al., 31 Aug 2026) in Section 1, subsection “Previous Work on \eqref{e.LFD}”