Plane waves in noncommutative fluids

We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy–momentum tensor of the plane waves is calculated. •We obtain the dynamics of the noncommutative fluid in the Snyder space at the first order in the power expansion in terms of the noncommutative parameter.•We solve the corresponding linearized equations of motion and show that the solutions are monochromatic waves with simple geometric interpretation.•We calculate the energy–momentum tensor of these solutions.