Optimal decay rates of a non-conservative compressible two-phase fluid model

2020/10/22 by Wang, Huaqiao, Wang, Juan, Wu, Guochun +1
#35K65 #35Q30 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.11509

Abstract

We are concerned with the time decay rates of strong solutions to a non-conservative compressible viscous two-phase fluid model in the whole space R3. 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-frequency and high-frequency decomposition, delicate spectral analysis and energy method based on finite induction.

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