I made up a new word
Since the word "support" comes from the Latin "su" (meaning up) and "port" (meaning PUSH), I really hate to use this word when discussing breath management because I think it may encouraging PUSHING. In my studio, we approach breath management through the technique known as appoggio, which is from the Italian "appoggiare," meaning to lean against. It's the muscle antagonism between your rib muscles and your obliques. But "engage the appoggio" is an awfully long thing to say so instead....
"appoggianate!"
"appoggianate!"