From: Frederiksen, Brian, edited by John Taylor. Arnold Jacobs: Song and Wind. Windsong Press, 1996.
A quote from Arnold Jacobs (Page 122):
“The most common problems I have seen over the last 60-odd years I have been teaching are with respiration and the tongue. Surprisingly enough, I rarely find problems with the embouchure. That might sound strange because people come to see me because of problems with their embouchure, but frequently it is the embouchure reacting to a bad set of circumstances and failing – it is simply cause and effect. If we change the cause of the factor, it is easy to clear up the embouchure. The embouchure is not breaking down, it is trying to work under impossible conditions. When you are starving the embouchure for air volume, giving it all sorts of air pressure but not quantity, it cannot work. Very quickly you will be struggling to produce your tone. Just increase your volume of air not by blowing hard, but by blowing a much thicker quality of air. Very frequently the air column is just too thin.”
So the air flow is key to a healthy embouchure. The lips and the air should have a symbiotic relationship; they depend upon one another.