Just about every house and even apartment I go into has a crack on the wall above a door or doors. Mostly in one of the corners above the door. When a building shifts cracks will commonly appear above doors by one corner or the other. The Earth is always moving and in some areas of the world it moves more often and is more noticeable than others. Where I live the Earth under our homes is hard clay so there is quite a bit of cracking going on in our homes. If you drive 10 minutes east of my City the ground is perfect for building and they dont have problems with cracking. Regardless if you have a crack to fix whether it is above your door or not I am going to tell you how to easily fix it so the crack does not come back that easily.
To fix the crack properly you will need a putty knife, a small container of pre-mixed joint compound, a piece of drywall tape either the paper type or the mesh type that sticks to the wall. You will also need a utility knife and some sort of drywall mud sander. I use a sanding block but you can use a piece of drywall compound sanding paper.
1) The first thing you need to do is take your utility knife and cut out the edges of the crack so there is a depression along the crack. (for example a valley not a hill) Usually when there is a structural crack in a wall there is a ridge sticking out. You want to get rid of the ridge so you can fill the crack and have a flat surface.
2) The next thing to do is take your pre-mixed drywall joint compound and spread some over the crack. Spread enough so it is wider than the width of your drywall tape and longer than the crack, go about 2 past each end of the crack. Spread 3 to 4 inches wider and a couple inches longer than the crack.
3) Now take your drywall tape and cut a piece that is longer than the crack but shorter than the swath of joint compound you just spread on the wall. Take your piece of tape and lay it over the crack. Holding one end down by pressing it with a finger take your putty or drywall knife with a bit of compound on the blade and wipe the tape so it lays flat. Wipe the area with your drywall knife that you were holding with your finger.
4) Go over the patch with your knife until you feel it is lying flat. Dont leave a mound of compound on the wall.
5) Repeat spreading drywall joint compound two more times increasing the width and length of the area each time. The wider you go the less pronounced the area will be when your job is done.
6) After you have two more coats on you can sand the area lightly so that there are no ridges and the area looks smooth and ready to prime and paint. Then youre done.
Rest assured that your crack will not reappear as easily as it would if you would have just patched the crack with joint compound alone. When your house shifts the crack under the drywall tape might move and spread but now that you have tape over it you will not notice it. You might see a slight ridge in the tape when the house shifts but that should be about it. You have now fixed the annoying crack above your doorway.