Uniform Decay for Ruggeri's Relaxed Navier-Stokes-Fourier Equations

This work studies the linearization of Ruggeri’s classical symmetric hyperbolic model of viscous, heat-conductive fluids about a homogeneous equilibrium. In three space dimensions, we show that perturbations in $L^1\cap L^2$ decay in $L^2$ at the rate $(1+t{)}^{-3\mathrm{/}4}$, uniformly as a common parameter scaling the three relaxation times tends to zero. The estimate controls the equilibrium variables together with the appropriately weighted stresses and heat flux, and has the same decay rate as the formal Navier–Stokes–Fourier limit.