First, states used to officially declare war against their opponents when their hostilities with each other reach to its peak but this trend changed after the Second World War. The element of surprise is widely used to subdue the enemy. For example, the imperialist Japan attacks on Pearl Harbor and the Nazi attack on Soviet Russia.
After WW-II the United Nation played its role in preventing war. All members of UN refrained from the use of force against the territorial legitimacy or political independence of any states. When the North Korean armed forces crossed the 38th parallel on June 25, 1950, without the official declaration of war it sabotages the efforts of UN. All the members of UN stood up against this act of aggression by North Korea. They passed the 84th resolution of the Security Council in the absence of the Soviet Union during the vote. US took the leadership role to defend South Korea under the UN flag.
At present, the situation is more complex and the North Korea is openly declaring in case of any action against them. After 2013 when sanctions approved by the Security Council against North Korea and their nuclear test, Kim Jong openly declare the use of a pre-emptive strike against the US with nuclear weapons. It was followed by a "Full War Declaration Statement" which is a violation of armistice that ended the first Korean War in 1953.
In 2013, North Korea also cut the hotline that is used as a mean of the communication between North Korea and South Korea. The hotline was reconnected after the few months when South Korea closed the joint Kaesong industrial complex in wake of the Kim Jung-un's fourth nuclear test in early 2016. North Korea protested the act by calling it as a Declaration of War and then cut the hotline.
The cutting of the hotline was alarming. The hotlines are used to prevent the accidental war. South Korea has a hotline with China and tried to reconnect with North Korea. The use of hotlines started in 1963, after the Cuban Missile Crisis. The two superpowers decided to have hotlines to talk to each other during the crisis at short notice to avert the potential nuclear war.
Detonation of a nuclear device
Second, if North Korea threatened to detonate the nuclear device in the atmosphere over the Pacific region. This act would shock the world as it is against the international norms and it had not been observed since 1980 when China tested their nuclear devices. It would violate international environmental law along with the laws of war and peace. Kim would start a war if he detonates the nuclear device in North Korea or within the territory of other countries. It includes the ocean spaces under their control and ocean territory of Guam.
Therefore, if the nuclear devices exploded in international territory for instance, the high seas, North Korea would face different set of rules. For example, Australia and New Zealand took France to the International Court of Justice for testing their nuclear devices in the atmosphere. The emission of the radiation affected the global environment and well being of the global community. According to the international Environmental agreements, it is prohibited to conduct nuclear test in atmosphere. North Korea is not a signatory of these agreements that are against the atmospheric nuclear testing. But their nuclear test in the atmosphere can cause significant environmental damage to other nations and they can be held responsible for damaging the global environment.
Shooting down an aircraft
Third, the North Korea would shot down aircraft in international airspace and territorial sea, 12 nautical miles/22.2km. In 1969, North Korea did shoot down an American spy plane by killing all 31 members on the plane. It was operating in international airspace. President Nixon did not respond to it with force due to a fear of the Soviet Union and China reaction over it. Around the 60 times, Russian military aircraft have been close to Alaska or near to the edge of Western Europe. But from last10 years have not shown any unpleasant incident such as planes would be intercepted and followed.
No state has shot down any plane for crossing their territorial airspace. To avoid such mistakes choreographed saber rattling and certain other rules are applied if the planes would not be invisible. In all cases, transponders and radios must be on. The flight plans are disclosed in advance. If Kim tries to shot down one of the American planes in international airspace like his grandfather Kim Il-sung did in past. It would be risky how President Trump will respond to it either by force or use other means to diffuse the situation.
To conclude, it is difficult to predict future war scenario between North Korea and the US. War is against the international precedents and any such action can disrupt the peace and stability of the world. There is dire need to resolve this conflict by other means rather than using force against any state. The role of Russia and China is crucial in determining the future of relations between the US and North Korea. Both countries are the major power player at a global level. The use of force against North Korea would be counterproductive. There is a need to resolve this conflict by peaceful means rather than using force.