No matter how fatigued your body is, your core should always remain stable. Core training should be done before, during, and after your main workout. Theoretically, every exercise is a core exercise.
One of the most important core stability exercises for runners is leg lowering. During let lowering, you will lay on your back, engaging your midsection by pressing your lower back flat against the ground. Point both legs straight up at the ceiling and flex your toes. While maintaining your abdominal contraction, take a deep breath in and slowly lower one leg to a hover over the ground as you exhale. Bring your leg to the starting position again on an inhale. Repeat a full set on one leg before performing the exercise on the opposite. Each repetition should come as low as you can to the ground without your lower back peeling off the floor and without your foot touching the ground.
As a Spartan, leg lowering is one of the most beneficial exercises you can do. Not only does it train the hips from rocking throughout running, it also helps to elongate your hamstrings allowing your body to stride longer and to pull more efficiently as you run up mountains and hills. This exercise is perfect for any injury prevention work and can be performed daily as a rejuvenation technique.