Fluid mechanics of photonic gas in nonlinear media

We consider a gas of photons propagating in a nonlinear medium. We show that when the nonlinear parametric processes are extremely frequent, the macroscopic momentum transport equation is analog to the Navier–Stokes equation for an ordinary fluid. Associated with the energy conservative equation, this equation allows us to predict the existence of “second sound” wave of energy photon density or of a shock wave for the photonic fluid.