Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity
Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity
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DOI：
10.1007/s40818-020-0076-1
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发表时间：
2020-06-01
期刊：
影响因子：
2.8
通讯作者：
Vicol, Vlad
中科院分区：
文献类型：
--
作者：
Beekie, Rajendra;Buckmaster, Tristan;Vicol, Vlad
构造了总能量有限且磁螺旋度不是时间常数函数的理想磁流体动力学方程的弱解。从泰勒猜想出发，证明了理想磁流体力学存在有限能量弱解，而这在无限电导率和零粘性极限下是不可能得到的。我们的证明是基于一个纳什型凸积分计划与间歇积木适应的几何形状的MHD系统。
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist finite energy weak solutions to ideal MHD which cannot be attained in the infinite conductivity and zero viscosity limit. Our proof is based on a Nash-type convex integration scheme with intermittent building blocks adapted to the geometry of the MHD system.