TEACHER: Okay. What's the problem?
STUDENT: It's weak and unfocused. How can I improve it?
TEACHER: Let's see. How often do you work on it?
STUDENT: hmm... never...
TEACHER (rolling his eyes): sigh...
Developing a good low register doesn't take as much strength and endurance as the high register but it does take some skills which you will need to develop over time.
We can talk for hours about the low embouchure versus the high embouchure, the break, dropping your jaw, putting pressure here and there but these things won't work if you don't spend time working on them.
We too often overlook low range practice because we think it's easy or not as important as the high range. The fact is that it isn't that simple and yes, it is important!
We all have a couple of notes that are a bit weaker than the others down there. This is the break or the place where we change from high to low embouchure and vice-versa. It's at a different place for everyone You will need to identify where is that break for you and practice switching from high to low position by slightly dropping your jaw (not too much!) when you pass the break on the way down and by bringing it up to normal on the way up.
How much you need to drop depends on you. Everyone is different so you'll have to experiment to see what is comfortable for you.
From then on, you can do long tones in the low register to focus your sound. You can also play some etudes or solo pieces an octave lower. Kind of weird but efficient! Practice a lot of scales going down every day and work on your low excepts. You can spend a lot of time doing this because it's not very tiring.
It's no use trying to force a lot of air in your instrument to play louder. You better focus on tone quality and intonation. You'll gradually get more power over time as your chops get used to play in that register.
When you do work on your low register, remember to practice your high register as well otherwise you'll be out of shape up there.