Nonspherically symmetric equilibrium bubbles in a steadily rotating incompressible fluid
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916861019422720 |
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| author | Lai, Chen-Chih Weinstein, Michael I. |
| author_facet | Lai, Chen-Chih Weinstein, Michael I. |
| contents | This note presents two nontrivial, rotational equilibrium solutions to the spatial uniform gas pressure (isobaric) approximate model of Prosperetti in the inviscid case. Building on Gavrilov's work [GAFA 2019], we first establish the existence of equilibrium solutions with nontrivial (rotational) liquid flow. Second, we construct a nonspherically symmetric, horn-torus-shaped equilibrium bubble under mild spatial decay conditions of the liquid flow. In addition, we extend earlier results on the characterization of spherical equilibrium bubbles to the axisymmetric, purely azimuthal setting. Finally, we implement a numerical simulation of the equilibrium bubble shape using the Physics-Informed Neural Network (PINN) approximation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonspherically symmetric equilibrium bubbles in a steadily rotating incompressible fluid Lai, Chen-Chih Weinstein, Michael I. Analysis of PDEs Mathematical Physics Pattern Formation and Solitons Fluid Dynamics This note presents two nontrivial, rotational equilibrium solutions to the spatial uniform gas pressure (isobaric) approximate model of Prosperetti in the inviscid case. Building on Gavrilov's work [GAFA 2019], we first establish the existence of equilibrium solutions with nontrivial (rotational) liquid flow. Second, we construct a nonspherically symmetric, horn-torus-shaped equilibrium bubble under mild spatial decay conditions of the liquid flow. In addition, we extend earlier results on the characterization of spherical equilibrium bubbles to the axisymmetric, purely azimuthal setting. Finally, we implement a numerical simulation of the equilibrium bubble shape using the Physics-Informed Neural Network (PINN) approximation. |
| title | Nonspherically symmetric equilibrium bubbles in a steadily rotating incompressible fluid |
| topic | Analysis of PDEs Mathematical Physics Pattern Formation and Solitons Fluid Dynamics |
| url | https://arxiv.org/abs/2507.17915 |