The Regularity of Weak Solutions of the 3D Navier–Stokes Equations in $${B^{-1}_{\infty,\infty}}$$
The Regularity of Weak Solutions of the 3D Navier–Stokes Equations in $${B^{-1}_{\infty,\infty}}$$
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DOI：
10.1007/s00205-009-0265-2
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发表时间：
2007-08
影响因子：
2.5
通讯作者：
A. Cheskidov;R. Shvydkoy
中科院分区：
文献类型：
--
作者：
A. Cheskidov;R. Shvydkoy
本文证明了如果三维Navier-Stokes方程的Leray-Hopf解属于或它在范数上的跳跃不超过粘性的常数倍，则u对（0，T]是正则的.我们的方法使用频率的非线性项的局部估计，并产生一个经典的Ladyzhenskaya-Prodi-Serrin准则的扩展。
We show that if a Leray–Hopf solutionuof the three-dimensional Navier–Stokes equation belongs toor its jumps in the-norm do not exceed a constant multiple of viscosity, thenuis regular for (0,T]. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya–Prodi–Serrin criterion.