Global Smooth Solutions in $\mathbb{R}^3$ to Short Wave-Long Wave Interactions Systems for Viscous Compressible Fluids

The short wave-long wave interactions for viscous compressible heat conductive fluids is modeled, following Dias and Frid [SIAM J. Math. Anal., 43 (2011), pp. 764--787], by a Benney-type system coupling Navier--Stokes equations with a nonlinear Schrodinger equation along particle paths. We study the global existence of smooth solutions to the Cauchy problem in $\mathbb{R}^3$ when the initial data are small smooth perturbations of an equilibrium state.