A strong core plays a crucial role in your running performance.
If you run with correct posture, your core will feel solid and you will get a corework out the entire run!
Here's an exercise for home
Bridges - Lie on the floor face up with your knee bent 90 degree and feet flat on the floor. Lift your hips and back off the floor until your body forms a straight line from your shoulder to your knees. Hold for 10secs. Lower slowly to the floor and repeat 10 times. Squeeze your glutes on the way up and activate your deep core to maintain the straight body during the 10 sec hold.
Make it a habit - do this exercise each night as you watch telly or before you hop into bed!