Global axisymmetric Euler flows with rotation

• 成果类型: Article
• 署名作者: Guo, Yan; Pausader, Benoit; Widmayer, Klaus
• 署名单位: Brown University; University of Zurich; University of Vienna
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01145-6
• 发表日期: 2023
• 页码: 169-262
• 关键词: gravity water-waves; finite-time singularity; Navier-Stokes equations; klein-gordon equations; 3d euler; classical-solutions; EXISTENCE; SYSTEM; REGULARITY; SCATTERING

摘要

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform rigid body rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. To establish this, we introduce a framework that builds on the symmetries of the problem and precisely captures the anisotropic, dispersive mechanism due to rotation. This enables a fine analysis of the geometry of nonlinear interactions and allows us to propagate sharp decay bounds, which is crucial for the construction of global Euler flows.