Both the place name sea of japan (name established by international organizations) as East Sea (name advocated by the two Koreas) are written with a lower case initial in the word mar.
However, phrases such as “Tension soars in the Sea of Japan” are sometimes found in the media, “The Japanese government said that missile launches in the East Sea violate Security Council resolutions of the UN” or “The storm has been felt mainly on the coasts of the Sea of Japan”.
According to Spelling of the Spanish languagelos names of geographical features composed of a generic noun (sea, river, volcano…) and a proper name (Mediterranean, Orinoco, Kilauea…) are normally written with the generic in lowercase.
Therefore, in the initial examples it would have been appropriate to write “Tension soars in the Sea of Japan”, “The Japanese government said that missile launches in the East Sea violate UN Security Council resolutions” and “The storm has been felt mainly on the coasts of the Sea of Japan.”
It is recalled that, to allude to this maritime zone between the eastern coast of the Asian continent and Japan, traditionally the name of sea of japanwhich is the recommended form in Spanish and also the one established by international organizations such as the International Hydrological Organization, so it is advisable to also reflect this form if you choose to give the preferred by North Korea and South Korea East Sea: «Two short-range ballistic missiles fall in the Sea of Japan (called East Sea in Corea)”.