In this paper we study the time decay rates of the solution to the Cauchy problem for the compressible viscoelastic flows via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, and the Ḣ⁻ˢ(0≤ s<3/2) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.
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Wu et al. (2016) studied this question.
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