All the zombies will probably rot, decay, and fall apart within a year. That, or they will end dying from hunger or thirst because no organism can survive without food or water.
Just remember to keep your eyes down range and finger on the trigger. When they get close we will rip off their skulls and toss them away laughing. Were going to blow them up with everything we got until we have nothing left to shoot them with, then we are going to strangle them with their own living guts!
To be fair, if you're going to have suspension of disbelief enough to accept Zombies, an undying collection of monsters immune to everything but total destruction of their brain caused by a virus spread only by bite (sometimes blood) or voodoo curse, then you kind of have to suspend your disbelief enough to accept that they mysteriously don't require water or food for energy, or that they're somewhat resilient to decay.
I mean, the decay side alone could be explained by the virus making the body poisonous to many bacteria species and animal detritivores.
And I suppose the food/water side if necessary could be provided by them eating humans and other animals. There's plenty of water in animal life.
And if you accepted a more unusual zombie story, like that of 28 Days Later, they know that "zombies" eventually starve to death. Taking, unsurprisingly, about 56 days (2 sets of 28, as there are 2 gaps of 28 days in the film at the beginning and end).