Non-uniqueness and h-Principle for Holder-Continuous Weak Solutions of the Euler Equations

被引:84
作者
Daneri, Sara [1 ]
Szekelyhidi, Laszlo, Jr. [2 ]
机构
[1] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany
[2] Univ Leipzig, Inst Math, D-04009 Leipzig, Germany
基金
欧洲研究理事会;
关键词
INCOMPRESSIBLE EULER; FLOWS;
D O I
10.1007/s00205-017-1081-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. We prove that the set of Holder wild initial data is dense in , where we call an initial datum wild if it admits infinitely many admissible Holder weak solutions. We also introduce a new set of stationary flows which we use as a perturbation profile instead of Beltrami flows in order to show that a general form of the h-principle applies to Holder-continuous weak solutions of the Euler equations. Our result indicates that in a deterministic theory of three dimensional turbulence the Reynolds stress tensor can be arbitrary and need not satisfy any additional closure relation.
引用
收藏
页码:471 / 514
页数:44
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