Abstract
This paper aims to give a detailed presentation of long-wave instabilities of shear layers for Navier-Stokes equations, and in particular to give a simple and easy-to-read presentation of the study of the Orr-Sommerfeld equation and to detail the analysis of its adjoint. Using these analyses, we prove the existence of long-wave instabilities in the cases of slowly rotating fluids, slightly compressible fluids or Navier boundary conditions, under smallness conditions.
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Acknowledgements
Dongfen Bian was supported by National Natural Science Foundation of China (Grant Nos. 11871005 and 12271032).
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Bian, D., Grenier, E. Long-wave instabilities. Sci. China Math. (2024). https://doi.org/10.1007/s11425-022-2148-2
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DOI: https://doi.org/10.1007/s11425-022-2148-2