Is there a way of installing crown made from wood/mdf on a curved wall?

It obviously depends upon the degree of arc... in other words, too much of a curve can be really hard to work with. I've back-cut anywhere from one blade width to about 1/4" in order to 'wrap' the wood to match a wall. If it's a convex situation you'll do just the opposite - and then use a wood putty product to make the cuts 'disappear' when you've finished. Also, I don't think MDF will be nearly as easy to work with as natural wood, but again it really is dependent on just how much bending is required.
Hope this helped!

I run a millwork faculty here in NJ.

There are very easy solutions in today's market for curved walls. We sell flexible moulding made of composite material in exact (or near exact) patterns.

Find out the radius of the wall, get the pattern # of the crown (WM47, WM49, etc). Then go to your nearest lumber yard and you can order flex moulding to that pattern.

There are several companies manufacturing it now. My preference is a company called Ultra Flex or Resin Flex (doesn't crack or crinkle so much). If the radius is tight have them preform it to your radius (it doesn't cost any extra)

Do a search for (flexible moulding) you will see many options available

We used to use the method that norcal spoke of but it really takes a lot of time and putty and sanding and more putty, the flex molding is expensive you may pay up to 100 for just 8ft or so, good luck, nichols trim