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Decay estimates to the inhomogeneous Navier–Stokes equations in \(\mathbb {R}^{3}\)

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Abstract

In this paper, we study the decay estimates to the inhomogeneous incompressible Navier–Stokes Equations in \(\mathbb {R}^{3}\). The greatest difficulty is that the density \(\rho \) has only \(L^{\infty }\) norm; to overcome, this difficulty we find a new key quantity \(\int ^{+\infty }_{0}\Vert u\Vert ^{2}_{L^{\infty }}\textrm{d}t< +\infty .\)

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Acknowledgements

Part of this work was done when Yanmin Mu visited Academy of Mathematics & Systems Science, The Chinese Academy of Sciences. We would like to thank Prof. Ping Zhang for valuable discussions. Y. Mu was partially supported by NSFC (Grant No.11701268), Natural Science Foundation of Jiangsu Province of China (BK20171040), and Chinese Postdoctoral Science Foundation (2018M642277).

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  1. School of Mathematical Sciences and Mathematical Institute, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Yanmin Mu

  2. School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing, 210046, People’s Republic of China

    Yanmin Mu

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  1. Yanmin Mu
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Mu, Y. Decay estimates to the inhomogeneous Navier–Stokes equations in \(\mathbb {R}^{3}\). Z. Angew. Math. Phys. 74, 121 (2023). https://doi.org/10.1007/s00033-023-02013-w

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