| Abstrakt: |
This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. 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 strong solutions via a standard continuity 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 all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of θ ∞ > θ I discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022). [ABSTRACT FROM AUTHOR] |
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