The Navier Stokes equations are differential equations that describe the flow of fluids with changes in density and temperature. They are used to describe weather or climate. They are non-linear, chaotic, with sensitive dependence on initial conditions.
That means, no finite description of a starting state, or any finite description of a number of starting states are sufficient to enable prediction of a long term future state.
This has been known since the 1963 paper by Edward Lorenz “Deterministic Aperiodic Flow”. It is a founding work in the study of chaos.
It took about 24 hours of computation time on a very serious supercomputer.
The world is a very big place, the vary few climate interaction sub models that have been characterized are also very non liner.
It's really tough to say about the interactions between the multitude of the climate interactions mechanisms that we don't yet realize exist along with the other mechanisms that we have a hazy realization of but have no realistic characterization or model pretty much makes any realistic analysis intractable.
I am not quite as arrogant as the Global Warming gurus so I have to admit I have absolutely no idea what realistic boundary conditions on a world wide scale might be or how to properly apply them. Given the complexity and scope of the problem and enormous size of the world, a slightly more humble perspective might be in order for some of the more vocal researchers.
The biggest factors are the amount of solar radiation energy that hits the earth and how much of that energy is either radiated or reflected back into space.
The amount of solar energy from the sun hitting the earth is constantly changing, we have no control over the sun, and very little ability to accurately predict what the sun's output will be over any extended length of time.
The amount of the sun's energy the Earth radiates and reflects back into space are not constants and the parameters that govern the reflection and radiation have not been sufficiently characterized to provide the input for an accurate, and possibly not even realistic basis for climate analysis.
Having tried my hand at Navier Stokes modeling in the past, let me add to what you said. As bad as Navier Stokes is to model, they are just a subset of the equations needed to do climate modeling. There are also chemical, phase shift, biological, etc. factors not even considered.
In other words, the only way for these computer models to be accurate to the degree these “environmentalists” claim, is for them to start by knowing the exact energy vector of every molecule of everything everywhere.
Translated into English, for those who don't speak PDE, these equations cannot predict how large a temperature change will result from very small changes in CO2, or even the direction of change. In chaos theory, the butterfly effect refers to a hurricane's formation depending on how many times a distant butterfly had flapped its wings several weeks before. In the correct application of math to global warming theory, the nature of the equations means that the extra CO2 emitted by a butterfly can change whether the earth warms or cools and can change that outcome in either direction.
This pretty much sums up the world-is-ending, humans-are-evil, surrender-to-the-world-bureaucracy, Chicken-Little Climate Crisis.