  The physical quantities in a gas should vary continuously across a shock.
However, the physics inherent in the compressible Euler equations is
insufficient to describe the width or structure of the shock. We demonstrate
the existence of weak shock profiles to the kinetic Landau equation, that is,
traveling wave solutions with Maxwellian asymptotic states whose hydrodynamic
quantities satisfy the Rankine-Hugoniot conditions. These solutions serve to
capture the structure of weak shocks at the kinetic level. Previous works
considered only the Boltzmann equation with hard sphere and angular cut-off
potentials.
