Onsager's Conjecture for Admissible Weak Solutions
Onsager's Conjecture for Admissible Weak Solutions
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DOI：
10.1002/cpa.21781
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发表时间：
2019-02-01
影响因子：
3
通讯作者：
Vicol, Vlad
中科院分区：
文献类型：
--
作者：
Buckmaster, Tristan;De Lellis, Camillo;Vicol, Vlad
我们证明了，给定任意时间间隔，给定任意光滑的能量分布，存在三维Euler方程的弱解，使得对于所有的。此外，我们表明，一个合适的原则，持有的正则类，任何。这意味着，我们构造的耗散解在某种意义上是在适当的子解空间中的典型解，而不仅仅是孤立的例子。
We prove that given any, a time interval, and given any smooth energy profile, there exists a weak solutionof the three-dimensional Euler equations such that, withfor all. Moreover, we show that a suitable-principle holds in the regularity class, for any. The implication of this is that the dissipative solutions we construct are in a sense typical in the appropriate space of subsolutions as opposed to just isolated examples.