Optimal Temporal Decay Rates of the Solution for Combustion of Compressible Fluids

This paper explores the Cauchy problem and temporal decay rates associated with the Navier-Stokes equations featuring reaction diffusion. Suppose that the initial data is a small perturbation near the equilibrium state ρ ∞ , 0, θ ∞ ,ζ), where ρ ∞ > 0, θ ∞ < θ I (the ignition temperature), and 0 < ζ≤ 1, we first establish the global-in-time existence of the strong solutions via a standard continued argument. With the additional L 1 -integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of the all-order derivatives of the strong solution. The work of this paper can be considered as the further investigation to [Wang-Wen, Sci. China Math. 65, 2022, 1199-1228].