How could Earth have two extremes of environment in the future even after pollution

[♥ Sherry ♥]

and nuclear war ? I have read predictions of the future that even after a large scale nuclear war and pollution, some parts of Earth would have an atmosphere so toxic as to require domed cities to protect from the poisonous air, while other parts of the Earth would be lush and green with a clean atmosphere. Would not pollution and nuclear fallout be worldwide?