I don't think the people terrible enough to launch nukes all other the place are in the position to do that. If the last 70 years are any indication, people don't tend to nuke other people.

There are nukes in Pakistan, India, Israel, Russia, other former Soviet countries, China, and US, all under increasingly fascistic rule. The orange baboon has publicly entertained using them just for dramatic effect. What do you imagine will restrain them as tensions resulting from mass migration, collapsing harvests, and desertification continue to grow?

Hey, with a bit of luck we'll get a nuclear winter which will counter global warming. -.-

You are being excessive.

First, why do you assume they would migrate north and not further south?

In your model do you expect people to move in or out of Australia, South Africa, Chile, etc. ?

Maybe because most of the land is in the north? This is not rocket science.

How does that change anything? Humanity could fit into a small island with the population density of dt Tokyo. There is plenty of land up, down, left and right.