Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces
Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces
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DOI：
10.1088/1361-6544/ab60d3
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发表时间：
2018-02
期刊：
影响因子：
1.7
通讯作者：
A. Cheskidov;Xiaoyutao Luo
中科院分区：
文献类型：
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作者：
A. Cheskidov;Xiaoyutao Luo
关于三维Navier-Stokes方程的Onsager猜想涉及到弱解在光滑性方面能量相等的有效性。本文建立了一类大函数空间中弱解的能量等式。这些条件是时间弱的，具有最优空间规则性，因此比以前的经典结果弱。给出了使用间歇论证和无发散反例的启发式方法，表明了我们的条件可能的尖锐性。
Onsager’s conjecture for the 3D Navier–Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note, we establish the energy equality for weak solutions in a large class of function spaces. These conditions are weak-in-time with optimal space regularity and therefore weaker than previous classical results. Heuristics using intermittency argument and divergence-free counterexamples are given, indicating the possible sharpness of our conditions.