关于磁螺旋度守恒的泰勒猜想的证明
Proof of Taylor's conjecture on magnetic helicity conservation
摘要：
我们证明泰勒的猜想，它说，在三维MHD，磁螺旋度是保守的理想极限在有界的，简单连接，完美的传导域。当磁畴是多连通时，磁螺旋度取决于磁场的矢势。在这种情况下，我们表明，磁螺旋度是保守的一个大的和自然类的矢量势，但不是一般的所有矢量势。作为泰勒猜想在二维中的一个类似，我们证明了均方磁势在理想极限下是守恒的，即使在多连通区域中也是如此。
英文摘要：
We prove Taylor's conjecture which says that in 3D MHD, magnetic helicity is conserved in the ideal limit in bounded, simply connected, perfectly conducting domains. When the domain is multiply connected, magnetic helicity depends on the vector potential of the magnetic field. In that setting we show that magnetic helicity is conserved for a large and natural class of vector potentials but not in general for all vector potentials. As an analogue of Taylor's conjecture in 2D, we show that mean square magnetic potential is conserved in the ideal limit, even in multiply connected domains.
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