DHL is F1's 'Logistics Partner' and they will move the essential kit (cars and mechanical components, garage and pitlane stuff) between the races not in Europe. The teams have several sets of less vital gear that moves by container ship (leapfrogging several races because of the time needed for the voyages) - partly because this method is a lot cheaper than air freight.

The 'behind the scenes' logistics of F1 is a massive operation, and there's an good explanation in this video. Although it focusses on two European races on consecutive weekends, there is plenty of detail about the 'flyaway' races.