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<p>The jet flow is one of the pivotal research issues in the field of free streamline theory and is closely related to physical phenomena such as oil drilling and rocket launch. It has consistently been a topic of interest for both the fluid dynamics and mathematics. In this paper, we analyze the geometric property of the free boundary for full compressible subsonic jet flow (without isentropic and irrotational assumptions), extending Li’s work&#xa0;(Math Methods appl sci, <a href="https://doi.org/10.1002/mma.10676">https://doi.org/10.1002/mma.10676</a>, 2025) on the well-posedness of the two-dimensional rotational subsonic jet flow for the compressible full Euler system. Specifically, we show that if the nozzle is concave toward the fluid, the free boundary of the jet flow is strictly convex to the fluid. Furthermore, we prove that the horizontal velocity in the fluid domain is always positive.</p>

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Geometric Property of the Free Boundary for Full Compressible Subsonic Rotational Jets

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  • 发表日期：

    2025年5月13日

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  • Xin Wang

摘要

The jet flow is one of the pivotal research issues in the field of free streamline theory and is closely related to physical phenomena such as oil drilling and rocket launch. It has consistently been a topic of interest for both the fluid dynamics and mathematics. In this paper, we analyze the geometric property of the free boundary for full compressible subsonic jet flow (without isentropic and irrotational assumptions), extending Li’s work (Math Methods appl sci, https://doi.org/10.1002/mma.10676, 2025) on the well-posedness of the two-dimensional rotational subsonic jet flow for the compressible full Euler system. Specifically, we show that if the nozzle is concave toward the fluid, the free boundary of the jet flow is strictly convex to the fluid. Furthermore, we prove that the horizontal velocity in the fluid domain is always positive.