Optimal decay rates of a nonconservative compressible two‐phase fluid model

Abstract

AbstractWe are concerned with the time decay rates of strong solutions to a nonconservative compressible viscous two‐phase fluid model in the whole space . Compared to the previous related works, the main novelty of this paper lies in the fact that it provides a general framework that can be used to extract the optimal decay rates of the solution as well as its all‐order spatial derivatives from one‐order to the highest‐order, which are the same as those of the heat equation. Furthermore, for well‐chosen initial data, we also show the lower bounds on the decay rates. Our methods mainly consist of Hodge decomposition, low‐ and high‐frequency decomposition, delicate spectral analysis, and energy method based on finite induction.