Nonspherically symmetric equilibrium bubbles in a steadily rotating incompressible fluid
Abstract
Abstract 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 approximation.
Fields of Study & Subjects
Fluid Dynamics and Heat Transfer
Navier-Stokes equation solutions
Fluid dynamics and aerodynamics studies
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 3
- Pages
- 035012–035012
- Publication date
- 12 March 2026
- Language
- EN