No rivers and no water is reality here for quite a while already. The islands rely a lot on desalination, and there is a big EU-funded project going on to create a desalination plant that not only is used to supply tap water, but the water basin of a new hydroelectric plant [0]. Desalination pretty much solves water issues, IF you have the energy (ideally renewable).

[0]: https://renewablesnow.com/news/construction-starts-on-200-mw...

Desalination solves water issues for tap water. Islands may be short on surface area.

I would also never use the word "solve", as this is just for human usage. The ecosystems themselves are irreversibly destroyed.