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A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations

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Abstract

In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier–Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura & Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, P. R. China

    Jiang Xu

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  1. Jiang Xu
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Xu, J. A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations. Acta. Math. Sin.-English Ser. 34, 662–680 (2018). https://doi.org/10.1007/s10114-017-7344-3

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