Catch up with who? If you mean USA, I will say ,Yes..
If you are talking about Russian or UK and France. No.
France can only manage to produce the pathetic M53 engines.
Same as UK Eurojet 200. 2 engines combined the most can only produced a medium weight jet fighter.. They are no way capable of producing a heavy weight engine of twins for F-22 class. Even the Russian 117S is just slightly higher than AL-31 engines. China WS-10G is probably same class like 117S engine.
Chinese WS-15 is going very smoothly and China has the money. What we have learn from WS-10 about making a modern high thrust turbofan has passed successful to make other project smoother and easier.
If you think WS-10 take long time to materialise will mean WS-15 having the same timeframe. Then I think you are very wrong. WS-10 is a very first attempt by Chinese in making a totally up to date modern turbofan. Of cos, problem bound to encounter and its difficult. But subsequent project will be easier with experience from WS-10 passed down to other class of engines..
So how fast China jump from developing J-10 to J-20. You can bet the lesson learn from J-10 was quickly absorb and practice on J-20.
Same can be apply on jet engines.
