Google Play is a digital distribution platform, which not only enables you to purchase application, but to store them in the cloud, since it is cloud based.
If the Youtube application crashes, then it is possible that another application to cause Youtube app failing.
You may try the following steps to make your app, any app, to work properly, such as:
- device rebooting
- check the system for updates (updates may fix app's problem, by providing enhancements);
- update the application
- remove temporary files from your device, to gain some space (this is a temporary solution)
- uninstall and then reinstall the application