Nonuniqueness of weak solutions to the Navier-Stokes equation
Nonuniqueness of weak solutions to the Navier-Stokes equation
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DOI：
10.4007/annals.2019.189.1.3
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发表时间：
2019-01-01
影响因子：
4.9
通讯作者：
Vicol, Vlad
中科院分区：
文献类型：
--
作者：
Buckmaster, Tristan;Vicol, Vlad
对于有限动能的初始基准，Leray在1934年证明了三维Navier-Stokes方程存在至少一个整体的时间有限能量弱解。本文证明了三维Navier-Stokes方程的弱解在有限动能弱解类中不是唯一的。此外，我们还证明了三维欧拉方程的Holder连续耗散弱解可以作为三维Navier-Stokes方程的一系列有限能量弱解的一个强消失黏度极限来得到。
For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Holder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.