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A Liouville type theorem for the stationary compressible Navier–Stokes equations

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Abstract

The present paper is dedicated to the Liouville type problem for the three-dimensional stationary barotropic compressible Navier–Stokes equations. We show that the velocity is trivial under some additional assumptions stated in terms of Lebesgue and \( \mathrm {BMO}^{-1} \) spaces.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The author appreciate the Editors and an anonymous reviewer for their valuable suggestions and constructive comments to improve the paper. This work was partially supported by the National Natural Science Foundation of China under the grants 11801443 and the Scientific Research Plan Projects of Shaanxi Education Department (CN) under the grants 22JK0475.

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  1. School of Mathematics and Statistics, Yulin University, Yulin, 719000, Shaanxi province, China

    Pan Liu

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Correspondence to Pan Liu.

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Liu, P. A Liouville type theorem for the stationary compressible Navier–Stokes equations. Anal.Math.Phys. 12, 121 (2022). https://doi.org/10.1007/s13324-022-00736-z

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  • DOI: https://doi.org/10.1007/s13324-022-00736-z

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