Finite-time singularity formation for C1,α solutions to the incompressible Euler equations on R3

• 成果类型: Article
• 署名作者: Elgindi, Tarek M.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.194.3.2
• 发表日期: 2021
• 页码: 647-727
• 关键词: navier-stokes equations; self-similar solutions; vorticity gradient; blow-up; exponential-growth; energy; FLOWS

摘要

It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D incompressible Euler equation is locally well-posed in the class of velocity fields with Ho center dot lder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.