go down vs go under

go down and go under both are verbs.

Word	Noun	Adjective	Verb	Adverb
go down	No	No	Yes	No
go under	No	No	Yes	No

As verbs, go down and go under are synonyms defined as:

Other synonyms of go down include settle, sink.

As verbs, go down and go under are synonyms defined as:

Other synonyms of go down include set.

As verbs, go under is a hyponym of go down; that is, go under is a word with a more specific, narrower meaning than go down:

go down (verb)	go under (verb)
grow smaller	be called; go by a certain name
stop operating	go under
be defeated	disappear beyond the horizon
be ingested
go under
disappear beyond the horizon
move downward and lower, but not necessarily all the way
be recorded or remembered