Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

• 成果类型: Article
• 署名作者: Jia, Hao; Sverak, Vladimir
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0468-x
• 发表日期: 2014
• 页码: 233-265
• 关键词: partial regularity

摘要

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.