An analysis of the 2-D isentropic Euler Equations for a generalized polytropic gas law
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914435642163200 |
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| author | Mello, Talita Neves, Wladimir |
| author_facet | Mello, Talita Neves, Wladimir |
| contents | In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the framework of the Euler equations expressed in self-similar variables and pseudo-velocities. A Bernoulli type equation is derived, serving as a cornerstone for establising a self-similar system tailored to rotational flows. We also developed an Ellipticity Principle for generalized polytropic gases, which is applied twice in this paper. To the best of the authors' knowledge, both applications appear for the first time. In particular, the analysis of the potential flow problem in the pseudo-subsonic regime is nontrivial for generalized polytropic gases when gamma< 1. In this setting, refined techniques, such as the Moser iteration method combined with suitable a priori estimates, are required. In the final section, the study extends to an analysis of a perturbed model, introducing the concept of quasi-potential flows, offering insights into their behavior and implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An analysis of the 2-D isentropic Euler Equations for a generalized polytropic gas law Mello, Talita Neves, Wladimir Analysis of PDEs 35L65, 35M30, 35Q31, 35Q35, 76N15 In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the framework of the Euler equations expressed in self-similar variables and pseudo-velocities. A Bernoulli type equation is derived, serving as a cornerstone for establising a self-similar system tailored to rotational flows. We also developed an Ellipticity Principle for generalized polytropic gases, which is applied twice in this paper. To the best of the authors' knowledge, both applications appear for the first time. In particular, the analysis of the potential flow problem in the pseudo-subsonic regime is nontrivial for generalized polytropic gases when gamma< 1. In this setting, refined techniques, such as the Moser iteration method combined with suitable a priori estimates, are required. In the final section, the study extends to an analysis of a perturbed model, introducing the concept of quasi-potential flows, offering insights into their behavior and implications. |
| title | An analysis of the 2-D isentropic Euler Equations for a generalized polytropic gas law |
| topic | Analysis of PDEs 35L65, 35M30, 35Q31, 35Q35, 76N15 |
| url | https://arxiv.org/abs/2506.23327 |