As Asia culture has its history roots of thousands of years, it has more experience and knowledge to keep the society more bonded and united together as a whole. The main reason Asia hasn't been one of leading nations were because they lived longer and has been through various ups and downs in their life cycle of economy. Once it starts to rise again it will stay for a long period. What do you guys think?
Anime have been manipulating the minds of youngsters and creating many fellow weeaboos and will continue to do so until all minds and linked with anime. DOKI DOKI was an interesting test and now we know it is possible for us to takeover your countries. The weeaboos will be the dominant race of society and there is nothing you can do to stop it.
The question is a bit strange, but I'm guessing the asker believes that American culture is dominant in Europe, and that in the future, Asian culture would replace this dominance. This argument is flawed in several respects:
1) American culture isn't exactly dominant in Europe
2) American culture is highly compatible with European culture
3) Asian culture itself is not homogeneous. South Asian culture (Indian culture) is different from Middle Eastern culture, which is different from East Asian culture.
Therefore, my answer to this question is threefold:
1) European culture will dominate Europe
2) American culture will continue to supplement European culture in Europe
3) Various forms of Asian culture will continue to have only distant outlier effects upon European culture.
I see this being true for the foreseeable future. After 50-100 years, there may be the possibility of the asker's scenario unfolding, but only if Asia as a whole becomes more homogeneous and somehow vastly outperforms economically vis a vis both Europe and America.