Peace in the surrounding waters maintained by self-restraint on the Japan side
It is well-known worldwide that Japan is currently in territorial disputes with three neighboring countries. These disputes concern the four northern islands, which are claimed by Russia, Takeshima, which cannot be effectively controlled due to Korean occupation, and Senkaku Island, which China is claiming territorial rights to but is currently controlled by Japan.
Since Korea is currently in control of Dokdo, the territory up to 12 nautical miles out from the island's east coast must also be Korean territory. However, Korea's claim of territorial rights to Dokdo was not recognized at the time maritime rights and the exclusive economic zone (EEZ) were determined. For this reason, ownership of the marine territory around Dokdo is uncertain, and as a result neither Korea nor Japan is able to conduct commercial fishing operations in the marine territory midway between the two countries, and it is currently a shared-use space which battleships and aircraft can freely pass in and out of.
If either country issued a prohibition to the other on the entry of ships and aircraft into the Dokdo surroundings, war would probably break out immediately. It's an extremely dangerous touch and go situation. Peace in the surrounding waters of Dokdo is being maintained by self-restraint on the Japan side.
In July 2006, Korea deployed numerous survey ships to carry out marine research activities in the surroundings of Dokdo. Although the Japanese government sent in the coast guard to block this, the president of Korea at the time, No Muhyon, gave an order to open fire and sink the coast guard ships. After finding this out, the Japanese government withdrew due to concerns the situation would escalate into armed conflict. This fact was later disclosed by Shinzo Abe, who was Chief Cabinet Secretary at the time.
Fortunately, the Japanese side noticed something unusual and withdrew the patrol boats, preventing a major incident. This incident shows that war could break out between these two military powers of East Asia at any time in the waters around Dokdo.
If a war were to break out between Japan and Korea related to the territorial rights for Dokdo, it would most likely end in an overwhelming victory for Japan. For both naval power and air power, Japan's military might is incomparably greater than Korea's. However, as long as the United States remains present in the area, there is likely no danger of escalation into all-out war.
If the cabinet support rates for the Japanese government were to drop drastically and the government made the decision to launch military actions for Dokdo in order to bolster support, this would have the benefits of enabling Japan to return Takeshima to Shimane Prefecture control and expanding its marine territory a great deal. On the Korean side, although the country would taste the humiliation of defeat, it would at the very least probably enable proper debate on which country's territory Dokdo really was to finally begin.