Robustness of one-dimensional viscous fluid motion under multidimensional perturbations

We adapt the relative energy functional associated to the compressible Navier–Stokes system to show stability of solutions emanating from 1-D initial data with respect to multidimensional N=2,3N=2,3 perturbations. Besides the application of the relative energy inequality as a suitable “distance” between two solutions, refined regularity estimates in LpLp based Sobolev spaces are used.