Strong abdominal muscles and a flat stomach are great to have, but it is more important to devote time to directly working the lower back muscles. Strong abs pull the torso forwards. If you have weak lower back muscles, there is nothing to help pull back against the spine, putting you at risk of developing poor posture and becoming hunched over. This can lead to lower back pain.
Think of the wires that support large radio towers as your muscles and the tower itself as your spine. If the wires pulling the tower in one direction are a lot stronger than the wires pulling it in the other direction, you’ll have a tower that will start leaning in the strong direction. The same thing happens with your core muscles and your spine.
Make sure you include some direct lower back training to help counterbalance your ‘core’ muscles (remember the ‘core’ goes right the ay around the body). Lower back exercises include hyperextensions, deadlifts, and reverse hyperextensions.