THESAURUS
buoy up
afford support, animate, back, back up, bear, bear up, bolster, bolster up, boost, brace, brighten, buoy, buttress, carry, cast up, cheer, cradle, crutch, cushion, elevate, encourage, enliven, erect, escalate, exhilarate, float, float high, give a lift, give support, gladden, hearten, heave, heft, heighten, heist, hike, hoick, hoist, hold, hold up, inspire, inspirit, invigorate, jerk up, keep afloat, keep up, knock up, lend support, levitate, lift, lift up, liven, lob, loft, mainstay, maintain, perk up, pick up, pillow, prop, raise, raise up, rear, rear up, reinforce, rejoice, rejoice the heart, ride high, rise, set up, shore, shore up, shoulder, sky, stay, stick up, subsidize, subvention, support, sustain, throw up, underbrace, undergird, underlie, underpin, underset, up, upbear, upbuoy, upcast, upheave, uphoist, uphold, upkeep, uplift, upraise, uprear, upthrow, vitalize, waft
ROGET THESAURUS
buoy up
Hope
VB
hope, trust, confide, rely on, put one's trust in, lean upon, pin one's hope upon, pin one's faith upon, feel hope, entertain hope, harbor hope, indulge hope, cherish hope, feed hope, foster hope, nourish hope, encourage hope, cling to hope, live in hope see land, feel assured, rest assured, feel confident, rest confident, presume, promise oneself, expect, hope for, anticipate, be hopeful, look on the bright side of, view on the sunny side, voir en couleur de rose, make the best of it, hope for the best, put a good face upon, put a bold face upon, put the best face upon, keep one's spirits up, take heart, take heart of grace, be of good heart, be of good cheer, flatter oneself, lay the flattering unction to one's soul, catch at a straw hope against hope, reckon one's chickens before they are hatched, count one's chickens before they are hatched, give hope, inspire hope, raise hope, hold out hope, promise, bid fair, augur well, be in a fair way, look up, flatter, tell a flattering tale, raise expectations (sentient subject), encourage, cheer, assure, reassure,
buoy up, embolden.