Onsager’s Conjecture for the Incompressible Euler Equations in the Hölog Spaces $$C^{0,\alpha }_{\lambda }(\bar{\Omega })$$
Onsager’s Conjecture for the Incompressible Euler Equations in the Hölog Spaces $$C^{0,\alpha }_{\lambda }(\bar{\Omega })$$
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Hölog 空间中不可压缩欧拉方程的昂萨格猜想 $$C^{0,alpha }_{lambda }(ar{Omega })$$
DOI：
10.1007/s00021-020-0489-3
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发表时间：
2019
影响因子：
1.3
通讯作者：
Jiaqi Yang
中科院分区：
文献类型：
--
作者：
H. B. Veiga;Jiaqi Yang
In this note we extend a 2018 result of Bardos and Titi \cite{BT} to a new class of functional spaces $C^{0,\alpha}_\lambda(\bar{\Omega})$. It is shown that weak solutions $\,u\,$ satisfy the energy equality provided that $u\in L^3((0,T);C^{0,\alpha}_\lambda(\bar{\Omega}))$ with $\alpha\geq\frac{1}{3}$ and $\lambda>0$. The result is new for $\,\alpha = \,\frac{1}{3}\,.$ Actually, a quite stronger result holds. For convenience we start by a similar extension of a 1994 result of Constantin, E, and Titi, \cite{CET}, in the space periodic case. The proofs follow step by step those of the above authors. For the readers convenience, and completeness, proofs are presented in a quite complete form.
In this note we extend a 2018 result of Bardos and Titi \cite{BT} to a new class of functional spaces $C^{0,\alpha}_\lambda(\bar{\Omega})$. It is shown that weak solutions $\,u\,$ satisfy the energy equality provided that $u\in L^3((0,T);C^{0,\alpha}_\lambda(\bar{\Omega}))$ with $\alpha\geq\frac{1}{3}$ and $\lambda>0$. The result is new for $\,\alpha = \,\frac{1}{3}\,.$ Actually, a quite stronger result holds. For convenience we start by a similar extension of a 1994 result of Constantin, E, and Titi, \cite{CET}, in the space periodic case. The proofs follow step by step those of the above authors. For the readers convenience, and completeness, proofs are presented in a quite complete form.
影响因子：
3
作者：
Buckmaster, Tristan;De Lellis, Camillo;Vicol, Vlad
通讯作者：
Vicol, Vlad