Abstract
Two conclusions have been achieved in this paper. Firstly, a formal solution of the equations\(\nabla \times \vec E = \vec \omega \),\(\nabla \cdot \vec E = P\) has been derived with different point of view from commonly known classical method developed by Helmholtz(1), (2), (3).
Secondly, a method to construct a vector field with given curl function and divergence function has been given in terms of the above solution.
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References
Coffin, J. G., Vector Analysis, New York, USA, (1911).
Cochin, N. E., Vector Calculus and Primary Tensor Calculus, Academy of Science, USSR (1951), 7th edition. (In Russian)
Fluid Mechanics, Edited by Department of Mathematics, Fudan University, (1960), Science and Technology Publishing House, Shanghai. (In Chinese)
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Communicated by Chien Wei-zang.
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Chun-bao, L. To construct a vector field with given curl function and divergence function. Appl Math Mech 2, 607–611 (1981). https://doi.org/10.1007/BF01895464
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DOI: https://doi.org/10.1007/BF01895464