If we step back and look at some history, classical music is deeply rooted on the European continent, but a fairly recent transplant in the New World. The UK is the odd man out. Music there was pursued with great energy and creativity during the Middle Ages and, right up to the death of Purcell in the late 17th century, was quite influential on European music. Then it seems to have died out, as a native pursuit, until the very late 19th century when Edward Elgar began the flourishing of classical music in 20th century Britain.
Similarly, classical, that is to say, notated concert music, has been pursued avidly in pockets of the New World, especially the US, Brazil and Argentina, during the 19th and 20th centuries. Indeed, composers like Philip Glass, Steve Reich and others are probably as important as any working today.
But it still remains the case that concert music has only very shallow roots everywhere in the world apart from Western Europe. What is happening in recent decades is that the thin veneer of Western European culture that has existed in a lot of the world is wearing away everywhere but in Western Europe. As an example, let's look at what inspired this post: the music page from the Canadian Broadcasting Corporation: http://www.cbcmusic.ca There are a host of items on the page, color-coded as to genre. Classical music items are aquamarine. On this whole page there are three classical items out of dozens and dozens of other genres.
The traditional expectation would be that a national broadcast network like the CBC or PBS in the US or ABC in Australia would have an educational or cultural mandate that would certainly include the promotion of classical or concert music. In recent decades this has been completely overturned and now these entities go out of their way not only to not promote classical music, but to bury it amid a wealth of non-classical music--to virtually no protest. On the European continent things are quite different as classical music is a core element of European national broadcast networks. It is also promoted by the BBC in the UK, again following a path a bit closer to the continent.
I suppose the big question mark today is what is happening in China where literally millions of young people are studying concert instruments like the piano and violin as well as the voice. How deeply will classical music root itself in China and will it be pushed to one side by popular forms as it seems to have been in South Korea?
Let's hear a clip of a performance by the very popular Chinese pianist Yuja Wang. Here she is playing the Piano Concerto No. by Chopin in Tokyo with the San Francisco Symphony conducted by Michael Tilson Thomas: