Peradzynski螺旋性定理的辛推广及其应用
A Symplectic Generalization of the Peradzynski Helicity Theorem and Some Applications
摘要：
本文提出了研究磁流体超流的辛对称分析方法，给出了Z。基于微分几何和群论方法，导出了Peradzynski螺旋性定理。本文在流形上微分几何结构的现代辛理论中重新分析了Peradzynski螺旋性定理，并对可压缩MHD超流情形给出了该定理的一个新的统一证明和一个新的推广。作为一个副产品，序列的非平凡的螺旋型局部和整体的不可压缩超流的情况下，发挥了至关重要的作用，研究在适当的边界条件下的稳定性问题的守恒律构造。
英文摘要：
Symplectic and symmetry analysis for studying MHD superfluid flows is devised, a new version of the Z. Peradzynski helicity theorem based on differential - geometric and group-theoretical methods is derived. Having reanalyzed the Peradzynski helicity theorem within the modern symplectic theory of differential- geometric structures on manifolds, a new unified proof and a new generalization of this theorem for the case of compressible MHD superfluid flow are proposed. As a by-product, a sequence of nontrivial helicity type local and global conservation laws for the case of incompressible superfluid flow, playing a crucial role for studying the stability problem under suitable boundary conditions, is constructed.
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