6 papers
Global smooth solutions to the inhomogeneous Landau-Fermi-Dirac equation
William Golding, Christopher Henderson
We consider the spatially inhomogeneous Landau-Fermi-Dirac equation with Coulomb potential, a quantum modification of the classical Landau equation for fermions. Mathematically, th…
On Hydrodynamic Implosions and the Landau-Coulomb Equation
William Golding, Christopher Henderson
We study the inhomogeneous Landau equation with Coulomb potential and derive a new continuation criterion: a smooth solution can be uniquely continued for as long as it remains bou…
Global regularity and decay estimates for the relativistic Landau equation
Christopher Henderson, Stanley Snelson, Andrei Tarfulea +1
We consider the relativistic Landau equation in the spatially inhomogeneous, far-from-equilibrium regime. We establish regularity estimates of all orders, implying that solutions r…
A Hamilton-Jacobi approach to road-field reaction-diffusion models
Christopher Henderson, King-Yeung Lam
We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a "thin-front limit," we are able to deduce a Hamilton-Jacobi eq…
A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation
Christopher Henderson, Giacomo Lucertini, Weinan Wang
In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on th…
Decay estimates and continuation for the non-cutoff Boltzmann equation
Christopher Henderson, Stanley Snelson, Andrei Tarfulea
We consider the non-cutoff Boltzmann equation in the spatially inhomogeneous, soft potentials regime, and establish decay estimates for large velocity. In particular, we prove that…