Existence of knotted vortex tubes in steady Euler flows

• 成果类型: Article
• 署名作者: Enciso, Alberto; Peralta-Salas, Daniel
• 署名单位: Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT)
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-015-0123-z
• 发表日期: 2015
• 页码: 61-134
• 关键词: diffeomorphisms; EQUATIONS; TOPOLOGY; Orbits

摘要

We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in . More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in , we show that they can be transformed with a C (m) -small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity. The structure of the vortex lines in the tubes is extremely rich, presenting a positive-measure set of invariant tori and infinitely many periodic vortex lines. The problem of the existence of steady knotted thin vortex tubes can be traced back to Lord Kelvin.