Geologically speaking, is there a risk that the Bosporus Strait and the Dardanelles Strait can close?

I don’t mean next week or next year.

It seems like the Black Sea (and by extension, the country of Georgia and several others) are heavily dependent on the Bosporus and the Dardanelles remaining open and navigable. But those of those straits are comparatively narrow.

Geologically, are the continents moving apart or together there? Is there a risk that at some point 50 million years from now that they will close? Since the Black Sea is a net outflow lake, would that then cause flooding in southern Russia?