It is my understanding that population growth is desirable for the economy. Are any economic theories that allowed for continued growth with a flat global population? Are there any ways to avoid significant short-term economic consequences?
Not problems - opportunities.
First, a lot of countries may resort to importing labour, thereby raising the economies of third-world countries (and so exacerbating the population implosion, as those countries become richer and stop growing). With a shortage of labour, there will likely be more investment in labour saving devices and automation. i.e. when dishwashers are hard to hire and wages go high, instead restaurants invest in automated dishwashing systems; same with many other businesses. wages go up, life is better all around for the working class. Unemployment is low.
Of course, there are unknowns. We have a boom generation of people who got decent wages, and many actually saved for retirement. What are the implications for the economy as they proceed to cash in on those savings? A glut of stocks on the market and depressed investment returns? What about houses? Do people want to buy 4-bedroom McMansions when hey have 1.2 children? What age will they move to a care home and try to sell the house? House prices to depress even more? A drop in house prices had a bad effect the last time.
There will be some adaption.
growth is not automatic, and growth is not always good, nor is lack of growth bad. A replacement economy will still exist. The question is, will we see the saga of Detroit - that it’s cheaper to move on, build fresh further away, and leave a mess for someone else, rather than spend the money to tear up the old and replace it? Will we see the return of urban decay on a massive scale?
part of it is an adjustment to understanding the market does NOT always expand. But maybe the automobile market is a good example, or the computer market. the vast majority of the markets there are replacement, as some things get old and obsolete and better products come out.