  Shock waves are an ubiquitous feature of hydrodynamic theories. Given that
fermionic quantum many-body systems admit hydrodynamical descriptions on length
scales large compared to the Fermi wavelength, it is natural to ask what the
status of shock waves is in such systems. Free fermions provide a solvable yet
non-trivial example, and here we generalise to include generic (non-integrable)
weak interactions to understand how a shock wave decays and changes its shape
well after forming.
