论文标题
Euler方程的非唯一性，直到Onsager的关键指数
Non-uniqueness for the Euler equations up to Onsager's critical exponent
论文作者
论文摘要
在本文中，我们处理了三维周期性环境中不可压缩的欧拉方程的库奇问题。对于Hölder持续可允许的弱解决方案，我们证明了$ l^2 $浓度的Hölder持续初始数据的$ l^2 $浓度的弱弱解决方案，这是对所有指数低于Onsager至关重要的$ 1/3 $的所有指数的连续初始数据。这改善了Daneri在Arxiv中获得的非独立性的结果：1302.0988以及Daneri和Szekelyhidi Jr.在Arxiv中：1603.09714，并概括了Buckmaster，De Lellis，Szekelyhidi Jr.和Vicol and arxiv：17001.08678的结果。
In this paper we deal with the Cauchy problem for the incompressible Euler equations in the three-dimensional periodic setting. We prove non-uniqueness for an $L^2$-dense set of Hölder continuous initial data in the class of Hölder continuous admissible weak solutions for all exponents below the Onsager-critical $1/3$. This improves previous results on non-uniqueness obtained by Daneri in arXiv:1302.0988 and by Daneri and Szekelyhidi Jr. in arXiv:1603.09714 and generalizes the result obtained by Buckmaster, De Lellis, Szekelyhidi Jr. and Vicol in arXiv:1701.08678.
