While attempting to play fluidly in the low register at a warm mezzo-forte, I found myself wanting to adjust to avoid cracked notes. I found myself pulling my embouchure back, which forced me to adjust within my mouth.
I know that being aware of the soft palate and the volume inside the mouth can increase resonance, so I reminded myself to "notice the soft palate," "allow the soft palate to lift."
(The soft palate is the "back" of the roof of the mouth. Trace your tongue along the roof of your mouth moving backwards. Towards the front, the roof of the mouth feels hard. As you move back, you reach a point where it becomes softer, almost squishy. This is the soft palate.)
Upon bring the soft palate into my awareness, I felt less need to pull my embouchure back. I had more control over my lips to shape the more fluid airstream that I was producing.
I find it helpful to picture the journey of the air while I breathe and play. I remind myself what movements are necessary to breathe, and I inhibit anything that could interrupt a natural breath, such as tension within the mouth.
Air comes first because it creates the sound. The lips shape the air.
This simple equation reminds me of the fundamentals while practicing, and helps me resolve issues such as cracked notes and lack of resonance.