Core Exercises
Why do them? Because the goal of core stability is to maintain a solid, foundation and transfer energy from the center of the body out to the limbs.
Core strengthening exercises are most effective when the torso works as a solid unit and both front and back muscles contract at the same time, multi joint movements are performed and stabilization of the spine is monitored. This doesn't mean you can't do crunches and bicycles. It just means that your core is much more than your abs
Muscles that accomplish this goal include:
Rectus Abdominis - located along the front of the abdomen, this is the most well-known abdominal muscle and is often referred to as the "six-pack" due to it's appearance in fit and cut individuals.
Erector Spinae - This group of three muscles runs along your neck to your lower back.
Multifidus - located under the erector spinae along the vertebral column, these muscles extend and rotate the spine.
External Obliques - located on the side and front of the abdomen.
Internal Obliques - located under the external obliques, running in the opposite direction.
Transverse Abdominis - located under the obliques, it is the deepest of the abdominal muscles (muscles of your waist) and wraps around your spine for protection and stability.
Hip Flexors - located in front of the pelvis and upper thigh. The muscles that make up the hip flexors include: psoas major, illiacus, rectus femoris, pectineus, sartorius
Gluteus medius and minimus - located at the side of the hip
Gluteus maximus, hamstring group, piriformis - located in the back of the hip and upper thigh leg
Hip adductors - located at medial thigh
Here are some core exercises (most are on youtube if you don't know how to do them):
Planks
Side Planks
Push Ups
Back Bridge
Hip Lift
Russian Twists
Squats
V-sits
Lunges
Side Lunges
Back Extensions
It goes without saying that you should never do an exercise if it hurts, so if the squats and lunges bother your knee, don't do them, or at least find a position and range of motion where it doesn't bother your knee. It's probably best to do those with a knee brace on ... Here are a couple of websites that shows most of what's out there:
This one looks pretty good, although depending on how bad your PFS is, you might want to get a physician's opinion:
You can also learn how to tape your knee, because that may be of more benefit to you right now than a brace (but without radiographs, it's tough to make a diagnosis). A physiotherapist or similar professional would be able to show you how to tape your knee. I can try to explain how to tape your knee by PM, but it might to easier if I can find some pics.
The physio clinic would also sell the Cover-Roll Stretch Tape and the Leukotape. But it might be cheaper online. I get all my rehab supplies from the sports physio clinic I go to, but the tape is sold on Amazon:
If you scroll down, they have a deal where you can get the 2" and 4" Cover-Roll tape plus the 1.5" Leukotape P. That's exactly what you want.