The Schrödinger-Navier-Stokes equation is formally equivalent to Navier-Stokes-Korteweg for capillary fluids at the action functional level, with dispersive and dissipative parameters controlling stiffness and damping in the derived sound-mode dispersion relation.
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Schr\"odinger-Navier-Stokes equation for capillary fluids
The Schrödinger-Navier-Stokes equation is formally equivalent to Navier-Stokes-Korteweg for capillary fluids at the action functional level, with dispersive and dissipative parameters controlling stiffness and damping in the derived sound-mode dispersion relation.