科研之友
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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.
- 出版日期2017-5
