The Euler equations as a differential inclusion

• 成果类型: Article
• 署名作者: De Lellis, Camillo; Szekelyhidi, Laszlo, Jr.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.1417
• 发表日期: 2009
• 页码: 1417-1436
• 关键词: incompressible euler; energy-dissipation; existence theorems; WEAK SOLUTIONS; CONSERVATION; FLOW

摘要

We propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in R-n with n >= 2. We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman concerning the non-uniqueness of weak solutions and the existence of energy-decreasing solutions. Our results are stronger because they work in any dimension and yield bounded velocity and pressure.