The Onsager conjecture in 2D: a Newton-Nash iteration

• 成果类型: Article
• 署名作者: Giri, Vikram; Radu, Razvan-Octavian
• 署名单位: Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01291-z
• 发表日期: 2024
• 页码: 691-768
• 关键词: ENERGY-CONSERVATION; WEAK SOLUTIONS; EULER; DISSIPATION; EQUATIONS

摘要

For any gamma<1/3, we construct a nontrivial weak solution to the two-dimensional, incompressible Euler equations, which has compact support in time and satisfies u is an element of C gamma(R(t)xT(x)(2)) . In particular, the constructed solution does not conserve energy and, thus, settles the flexible part of the Onsager conjecture in two dimensions. The proof involves combining the Nash iteration technique with a new linear Newton iteration.