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Regularity criteria and Liouville theorem for 3D inhomogeneous Navier–Stokes flows with vacuum

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Abstract

In this paper, we investigate the 3D inhomogeneous Navier–Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution \((\rho , u)\) satisfies suitable conditions.

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Acknowledgements

We would like to appreciate the anonymous referee for valuable comments. Jae-Myoung Kim was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2020R1C1C1A01006521).

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  1. Department of Mathematics Education, Andong National University, Andong, 36729, Republic of Korea

    Jae-Myoung Kim

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Kim, JM. Regularity criteria and Liouville theorem for 3D inhomogeneous Navier–Stokes flows with vacuum. Arch. Math. 121, 89–98 (2023). https://doi.org/10.1007/s00013-023-01860-3

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