According to the international law of passage, 12 nautical miles belongs to the territorial sea. The farthest distance between the Bohai Mouth island and Dalian is about 41.7 kilometers, which translates to
22.5 nautical miles (length of the yellow line in the map below) . Both sides extend 12 nautical miles, the Bohai Mouth just ties up, and any point on this line is China's territorial sea.
Look at the map below, all land and water left side of the redline is Chinese territorial water and land, in accordance to international law. And since Bohai sea is surrounded at all sides by Chinese territorial land and territorial sea, it is thus an internal sea ( same as a lake surrounded at all sides by territorial land) of China.
And yes, permission is require to enter Bohai sea.
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