Global existence of solutions to the compressible Navier–Stokes equation around parallel flows

The initial boundary value problem for the compressible Navier–Stokes equation is considered in an infinite layer of Rn. It is proved that if n⩾3, then strong solutions to the compressible Navier–Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations, provided that the Reynolds and Mach numbers are sufficiently small. The proof is given by a variant of the Matsumura–Nishida energy method based on a decomposition of solutions associated with a spectral property of the linearized operator.