Compressible Navier–Stokes Equations with Zero Heat Conductivity

We study the large-time behavior of solutions of the compressible Navier–Stokes equations without heat conductivity. Acoustic waves are dissipative due to the viscosity. Entropy waves are nondissipative due to lack of heat conductivity. Thus the system is of composite type, the simplest prototype of this class of nonlinear partial differential equations. We study the nonlinear interactions of waves using a combination of energy method, weighted energy method, and pointwise estimates.