| Abstract: | This paper is concerned with the study of the Cauchy problem to a multi-dimensional P1-approximation model. Based on a known global well-posedness (Danchin and Ducomet in J Evol Equ 14:155–195, 2014), in $$L^{2}$$-critical regularity framework the time decay rates of the constructed global strong solutions are obtained if the low frequencies of the data under a suitable additional condition. The proof mainly relies on an application of Fourier analysis to a mixed parabolic-hyperbolic system, and on a refined time-weighted energy functional. As a by-product, those time-decay rates of $$L^{q}$$–$$L^{r}$$ type are also captured in the critical framework. |
