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The well-posedness of incompressible rotational jet flows with gravity

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Abstract

This paper is concerned with the well-posedness theory and geometric property of steady two-dimensional incompressible jet flow with vorticity and gravity. The main results show that for given incoming mass flux and atmospheric pressure at outlet, there exists a unique incompressible jet flow issuing from a semi-infinitely long nozzle, and the free boundary initiates smoothly at the separation point. Moreover, we obtain the single intersection property of the free boundary by under-over theorem. As a consequence, the monotonicity of the free boundary will be established.

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Acknowledgements

The authors thank the anonymous referees for careful reading and for the valuable comments.

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  1. Department of Mathematics, Sichuan University, Chengdu, 610065, People’s Republic of China

    Jianfeng Cheng & Zhenlei Pei

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  1. Jianfeng Cheng
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  2. Zhenlei Pei
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Correspondence to Zhenlei Pei.

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Communicated by O. Savin.

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This work is supported in part by National Key R &D Program of China (No. 2022YFA1007700), National Natural Science Foundation of China (Nos. 12001387, 12371237), Sichuan Youth Science and Technology Foundation (No. 2021JDTD0024) and Sichuan Natural Science Foundation (No. 2023NSFSC1364).

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Cheng, J., Pei, Z. The well-posedness of incompressible rotational jet flows with gravity. Calc. Var. 63, 50 (2024). https://doi.org/10.1007/s00526-024-02661-4

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