Per the third act of the film, the breach is normally a one-way doorway.
It only allows kaiju to go back through it.
Given that at the end of the film, the jaeger was able to tag along with the kaiju when it went back through the breach, it's safe to assume that some water would also go through with them.
But it wouldn't be a constant flow into the breach, water would only go through when a kaiju did.
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The Breach appeared, at least to me, to be a one way barrier preventing anything not from the Anteverse to pass backward through to the alien universe.
But we are also forgetting that the Kaiju appear to swim from their universe to ours and appear perfectly adapted for living on Earth.
The Breach (also known as the Portal), is a fissure located off the coastline of China near Guam on the floor of the Challenger Deep of the Pacific Ocean.
It connects the Earth to the Anteverse; the homeworld of the Precursors and the Kaiju.
The Kaiju facility in the Anteverse appears to be underwater, as Gipsy Danger "floats" down after entering the Breach.
However, it is not; the facility simply has an artificially generated gravity column to allow access to the breach mechanism entrance .
This would mean the barrier doesn't have to work very hard because there is already equalized pressures on both sides, preventing water from rushing from our universe to theirs and vice versa except when a Kaiju crosses over.
Most importantly, the Precursors do not want to empty our oceans into their world.
They want to empty our world of life and migrate here.
Earth was likely chosen because of our great oceans, active tectonic plate structures (which power the Breach on our side), and the overall fragility of life on Earth.
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How are all these aquatic kaiju coming through if there is no water on the other side?
I think the answer is simply that: the water doesn't rush in because there is already water on the other side.
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There most definitely is water on both sides....
The Kaiju are aquatic, they swim up to and through the breach.
The Escape pods clearly rise due to the flotations devices attached to them when ejected from the Jaeger, which would indicate the presence of water.
The Jaeger clearly drifted down through the water when it was sinking into the Anteverse, as opposed to its fall from 50,000ft. & the icing on the cake....
when the reactor is going to explode, in the last scenes before the escape, you can clearly see water rushing into the mech from damage to the exterior.
Will one of the above posters, claiming that there isn't water on the other side of the breach, please explain why there would be water filling the mech and spraying around inside the Jaeger if it was not submerged?
(Don't tell me its left over from the ocean, it is clearly under pressure when sinking to the bottom of the Anteverse.)
That's a wrap!
P.s.
I just watched the movie again, when Mako's escape pod is released, a bunch of bubbles can clearly be seen escaping the Jaeger with the pod.
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Maybe the "portal" mechanism of the Precursors in the Anteverse have a way of floating the huge kaiju to exit their "portal" mechanism into our world & if the kaiju were to return to Anteverse, wouldn't the Precursors want their kaiju to float back down gently to their facility instead of free falling & the kaiju die with a huge 'PLOP!'
.... that would explain why Gipsy Danger floats down slowly in the ending scene before it explode.
As with the escape pod... the momentum from ejecting from the robot's head plus the "floating gravity" effect allows it to exit from the portal mechanism back into our world with quick pace and able to outrun the explosion.
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You could say the same thing about whatever surrounds the other side of the portal.
Water would only go into the portal if there was a space to fill i.e. the other universe has a gas atmosphere or is a vacuum.
So the other universe is either filled with (near the portal) a liquid with a density similar to saltwater or the pressures of the substances around both sides of the portal are equal, meaning our stuff won't pass through into theirs & vice versa.
Unless the Precursors allowed any particles to accompany the kaiju.
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In the movie Pacific Rim, the breach is located at the bottom of the ocean.     This breach is a wormhole/portal/gateway to some other universe that giant monsters freely move though back and forth.   What keeps our ocean from just emptying itself into this breach or their atmosphere rushing out?
In Pacific Rim what is keeping the ocean from rushing into the breach
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<pacific-rim>
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The breach can be seen as a one-way barrier. Another theory is that there is already water or a liquid with a similar density on the other side, and the resulting equal pressure prevents movement from one side to the other. The breach is a one-way barrier supported by water on the other side which means the pressures are balanced and the breach is a one-way doorway. 
The breach is a one-way barrier supported by water on the other side. This means the pressures are balanced and the breach is a one-way doorway. 