Formation of singularities for a transport equation with nonlocal velocity

• 成果类型: Article
• 署名作者: Córdoba, A; Córdoba, D; Fontelos, MA
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.162.1377
• 发表日期: 2005
• 页码: 1377-1389
• 关键词: 3-dimensional vorticity equation; one-dimensional model; 1d model

摘要

We study a ID transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.