The phrase "well up" typically conveys emotions of rising to the surface or filling up. There are several antonyms to this phrase, including phrases like dry up, empty out, subside, and recede. Dry up refers to the process of something becoming dry and ceasing to exist, which is the opposite of filling up. Empty out refers to the process of something becoming empty or being emptied, which is the opposite of something filling up. Subside means to become less intense, which is the opposite of something increasing in intensity. Finally, recede means to move away or become less visible, which is the opposite of something becoming more visible.