标题： 非球对称的平衡气泡在稳定旋转的不可压缩流体中 显示英文标题

标题： Nonspherically symmetric equilibrium bubbles in a steadily rotating incompressible fluid

摘要： 本注释展示了在无粘情况下Prosperetti的空间均匀气体压力（等压）近似模型的两个非平凡的旋转平衡解。 基于Gavrilov的工作[GAFA 2019]，我们首先建立了具有非平凡（旋转）液体流动的平衡解的存在性。 其次，我们在液体流动的温和空间衰减条件下，构建了一个非球对称的喇叭环面形状的平衡气泡。 此外，我们将早期关于球对称平衡气泡表征的结果扩展到了轴对称、纯方位角设置。 最后，我们使用物理信息神经网络（PINN）近似方法实现了平衡气泡形状的数值模拟。 显示英文摘要

摘要： 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.