Landau instability of strongly-coupled superfluids from hydrodynamics

Hydrodynamics provides an effective description of superfluids at scales large compared to the local equilibration scales. It is well-known that superfluids become unstable when a sufficiently large superfluid velocity is turned on. In this talk, I will explain how this instability can be captured within hydrodynamics, giving a simple expression for the critical velocity in terms of thermodynamic data. I will demonstrate that this is the mechanism responsible for the Landau instability in strongly-coupled superfluids constructed using Gauge/Gravity duality. This is in contrast to Helium 4 where rotons are responsible for the instability.