Indoor Core Workouts
If you are looking for indoor core workouts and the equipment to go with them, you might want to look into the TRX Suspension Trainer. It comes with all the equipment you need, as well as workouts and an app to help you along the way. However, there are also core workouts you can do at home with very little or no equipment at all. The beauty of this is that once you start working on your core, you will want to expand your workout to fine tune other areas of your body.
Breathing
Almost any trainer for any type of physical fitness regimen is going to tell you that breathing is one of the most important elements of working out. For one thing, you can monitor it to determine how healthy your workout is and how much you have progressed. The rule of thumb is that if you can't carry on a conversation, you are breathing too hard and need to slow down a bit. However, there is also something to be said for putting all of your focus into your breathing. It allows you to focus completely on your core and really notice details about your body. Practicing correct breathing methods also forces you to straighten your posture and open your diaphragm.
Replace Furniture
Pressed for time? Why not workout without even thinking about it? Try replacing some of your furniture with a stability ball. This is especially useful if you work at a desk and replace your chair with the stability ball. Instead of hunching over or leaning back, the ball forces you to focus on balance and posture. When you do want to work out, this is the perfect tool for core exercises.
Plank it Up
Planking has become immensely popular, with good reason. It requires no equipment
at all, though you can add some i you like. 
Essentially, you lay with your face toward the floor. Place your forearms on the floor so that your elbows are directly below your shoulders. Other than your forearms, only your toes should be touching the floor.Hold that position for as long as you can, then hold it for a few seconds longer. As you begin to be able to hold the position for longer intervals, you can make it more challenging. Considering elevating your legs to a chair rather than the floor. Do reverse leg lifts as you plank. Add weights to various areas of your body. All of these things can combine to create stellar workouts with obvious results.