Wave propagation for the compressible Navier–Stokes equations

Abstract

We establish the pointwise description of solutions to the isentropic Navier–Stokes equations for compressible fluids in three spatial dimensions. First, we give an explicit construction of the Green function for the linearized system. The Green function consists of singular waves, which dominate the short-time behavior, while the low frequency waves, the dissipative Huygens, diffusion and Riesz waves representing the large-time behavior. The nonlinear terms are treated by a suitable combination of energy estimates and pointwise estimates using the Duhamel's principle for the Green function.