Nonuniqueness of weak solutions to the Navier-Stokes equation

• 成果类型: Article
• 署名作者: Buckmaster, Tristan; Vicol, Vlad
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.189.1.3
• 发表日期: 2019
• 页码: 101-144
• 关键词: partial regularity; energy-conservation; onsagers conjecture; mild solutions; uniqueness; DISSIPATION; posedness; pressure; PROOF

摘要

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.