Global regularity for the spatially inhomogeneous Landau equation

Establish global regularity for the Landau equation with general spatially inhomogeneous initial data beyond the spatially homogeneous setting.

Background

The paper places the linear stability analysis of traveling Maxwellians within the broader theory of the Landau equation. Although global regularity has recently been established for spatially homogeneous very soft potentials, the corresponding problem for spatially inhomogeneous solutions with general data remains unresolved. The authors note that existing inhomogeneous results generally assume a priori pointwise control of hydrodynamic quantities or address particular types of singularities, rather than proving global regularity for arbitrary large data.