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- W1994171408 abstract "The Yang-Mills equation in Minkowski space with given initial data is considered. The gauge group is formulated in terms of Sobolev-Banach-Lie group, and the Cauchy problem for the equations thereby reduced to the temporal (hamiltonian) gauge. Given data for which are square-integrable over have respectively one and two derivatives which are square-integrable over space, a strong solution exists throughout space in a nontrivial time interval. If the initial data are infinitely differentiable in L2, the solution may be represented as a C∞ function on space-time satisfying the equations in the elementary sense. Strong solutions which agree at one time and have square-integrable derivatives as earlier agree throughout their regions of definition. For arbitrary finite-energy Cauchy data, there exists a quasi-solution (weak limit of solutions of truncated equations) which is global on Minkowski space. The solutions may take values in an arbitrary separable Hilbert Lie algebra." @default.
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- W1994171408 date "1979-08-01" @default.
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- W1994171408 title "The cauchy problem for the Yang-Mills equations" @default.
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- W1994171408 doi "https://doi.org/10.1016/0022-1236(79)90110-1" @default.
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