C-infinity Smoothing for Weak Solutions of the Inhomogeneous Landau Equation

We consider the spatially inhomogeneous Landau equation with initial data that is bounded by a Gaussian in the velocity variable. In the case of moderately soft potentials, we show that weak solutions immediately become smooth, and remain smooth as long as the mass, energy, and entropy densities remain under control. For very soft potentials, we obtain the same conclusion with the additional assumption that a sufficiently high moment of the solution in the velocity variable remains bounded. Our proof relies on the iteration of local Schauder-type estimates.National Science FoundationNational Science Foundation (NSF) [DMS-1246999]; NSFNational Science Foundation (NSF) [DMS-1907853]; Ralph E. Powe Award from ORAU12 month embargo; published online: 6 November 2019This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu