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Adverb usage meaning "to get under way" or "to be under way" widely favors two words in reference to something in motion, in progress, or in operation:
the meeting was under way by nine o'clock
The adjective usage is one word and generally descriptive of something in motion:
underway aerial refueling
Do not use under weigh in nautical sense when under way is meant; it does not mean anchors aweigh.