Time-Asymptotic Expansion with Pointwise Remainder Estimates for 1D Viscous Compressible Flow

Abstract We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier–Stokes equations. The leading-order term is the well-known diffusion wave and higher-order terms are newly introduced family of waves which we call . In particular, these provide an accurate description power-law asymptotics solution around origin $$x=0$$ x = 0 , where decays exponentially. valid locally also globally in $$L^p({\mathbb {R}})$$ L p ( R ) -norm all $$1\le p\le \infty $$ 1 ≤ ∞ proof based on Green’s function.