Anatomically the lower and upper abs is the same muscle, the rectus abdominis (the six pack).
A connection exist between the rectus abdominis and the hip flexors.
The hip flexors try to tilt the pelvis forward (anterior) whereas the rectus abdominis try to tilt the pelvis backward (posterior):
"FIGURE 2. The synergistic action of one representative abdominal muscle (rectus abdominis) is illustrated while lifting the right lower limb. (A) With normal activation of the abdominal muscles, the pelvis is stabilized and prevented from anterior tilting by the downward pull of the hip flexor muscles. (B) With reduced activation of the abdominal muscles, contraction of the hip flexor muscles is shown producing a marked anterior tilt of the pelvis (increasing the lumbar lordosis). The reduced activation in the abdominal muscle is indicated by the lighter red color."(1)
"Any muscle that is capable of flexing the hip from a femoral-on-pelvic perspective has a potential to flex the hip from a pelvic-on-femoral rotation. for this reason, tightness of secondary hip flexors, such as adductor brevis, gracilis, and anterior fibers of the gluteus minimus, would, in theory, contribute to an excessive anterior pelvic tilt and exaggerated lumbar lordosis."(1)
So tight hip adductors and weak rectus abdominis may cause anterior pelvic tilt.
Altough not explicitly stated in (1) I would think weak rectus abdominis may cause anterior pelvic tilt, which in turn may cause the hip adductors to become tight due to being chronically shortened.
There also exist a functional connection between the obliques and the hip adductors.
Consider a person running:
The left side of his pelvis is forward of the right side of his pelvis.
In order to bring his right leg forward he need to rotate the pelvis so that the right side of his pelvis is forward of the left side of his pelvis.
The oblique muscles on his left side work together with the adductors of his right leg to do this.
This system of muscles is called the Anterior Oblique Sling.
If the obliques are weak the adductors have to work more.
Further in an interesting article(2) Dean Somerset states that:
- hip internal rotation impairment correlates to lateral stabilization
- hip external rotation impairment correlates to anterior
stabilization (rectus abdominis)
The article seems credible but I have not been able to understand it yet.
However my conclusion on all this is:
if you have any tightness in the hips try strengthening the rectus abdominis and the obliques.
(1) Kinesiology of the Hip: A Focus on Muscular Actions
(2) The Side Plank for Internal Rotation Question