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The Yang-Mills and Yang-Mills-Higgs equations in temporal gauge are locallywell-posed for small and rough initial data, which can be shown using the nullstructure of the critical bilinear terms. This carries over a similar result byTao for the Yang-Mills equations in the (3+1)-dimensional case to the moregeneral Yang-Mills-Higgs system and to general dimensions.

Local well-posedness for the (n+1)-dimensional Yang-Mills and Yang-Mills-Higgs system in temporal gauge