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Decay Rates for Strong Solutions to the Compressible Navier–Stokes Equations without Heat Conductivity

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In this paper, we consider the compressible Navier–Stokes equations without heat conductivity in \({\mathbb {R}}^{3}.\) The global existence and uniqueness of strong solutions are established when the initial value towards its equilibrium is sufficiently small in \(H^{2}({\mathbb {R}}^{3}).\) The key uniform bound of entropy is obtained, even though the entropy is non-dissipative due to the absence of heat conductivity. Moreover, the time decay rates of global solutions are also given.

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Acknowledgements

W.L. Li, Y.H. Wang and L. Yao are supported by the Natural Science Basic Research Plan for Distinguished Young Scholars in Shaanxi Province of China (Grant No. 2019JC-26) and National Natural Science Foundation of China #11931013. W.J. Wang is supported by the National Natural Science Foundation of China #11871341,12071152.

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Authors and Affiliations

  1. School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi’an, 710127, China

    Weilong Li & Lei Yao

  2. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Wenjun Wang

  3. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Yinghui Wang

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  1. Weilong Li
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  2. Wenjun Wang
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  3. Yinghui Wang
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  4. Lei Yao
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Correspondence to Lei Yao.

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Communicated by I. M. Gamba

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Li, W., Wang, W., Wang, Y. et al. Decay Rates for Strong Solutions to the Compressible Navier–Stokes Equations without Heat Conductivity. J. Math. Fluid Mech. 23, 61 (2021). https://doi.org/10.1007/s00021-021-00590-2

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