亥姆霍兹分解

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物理学数学中的矢量分析中,亥姆霍兹定理英语Helmholtz's theorem),或称矢量分析基本定理fundamental theorem of vector calculus),宣称对于任意足够平滑、快速衰减的三维矢量场可解为一个保守矢量场和一个螺线矢量场的和,这个过程被称作亥姆霍兹分解英语Helmholtz decomposition)。

这意味着任何矢量场F,都可以视为两个势场(标势φ矢势A)之和。

参考文献[编辑]

  • George B. Arfken and Hans J. Weber, Mathematical Methods for Physicists, 4th edition, Academic Press: San Diego (1995) pp. 92–93
  • George B. Arfken and Hans J. Weber, Mathematical Methods for Physicists International Edition, 6th edition, Academic Press: San Diego (2005) pp. 95–101
  • C. Amrouche, C. Bernardi, M. Dauge, and V. Girault. "Vector potentials in three dimensional non-smooth domains." Mathematical Methods in the Applied Sciences, 21, 823–864, 1998.
  • R. Dautray and J.-L. Lions. Spectral Theory and Applications, volume 3 of Mathematical Analysis and Numerical Methods for Science and Technology. Springer-Verlag, 1990.
  • V. Girault and P.A. Raviart. Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms. Springer Series in Computational Mathematics. Springer-Verlag, 1986.

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