Not if you’re a dying samurai!
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can you elaborate in a compact nutshell what this equations seeks for?
the path of a fluid particle affected by forces, pressures and temperature fluctuations in any given time and space of that said fluid.
There are different approximations but no real solution.
BTW, this problem affects so many disciplines that solving this might as well get you a Nobel prize so 2 mills in the bank 
why is it not possible? does the math get to complex to resolve? the forces should merely equalise in the end thats it? you have very specific circumstances, with very specific energy potentials which can be precisely calculated. besides the maths which i am not good at it does not sound very complicated… sorry if that sounds totally noobish.
i am certain somebody with an overal understanding creative enough coupled with somebody well trained in maths should solve that in a jiffy.
People have been trying for over 100 years I think.
It’s a stochastic problem, you can solve it in an isolated piece of the fluid but not for the whole. In order to solve it currently with CFD they assume a lot of things like solving the issue for ideal fluid, incompressible, inviscid, isothermal, etc.
is that a general expression for a problem of such kind?
so what this equation should do is trying to precisely predict the direction of the flow as you say. but in which cases does this prediction fail?
what does “whole” mean?
does trying to calculate it nowadays involve quantum mechanics?
Long term large scale fluid - e.g. predicting weather for more than a week, or really a couple of days. Just take a look at the hurricanes. They are “born” in the ocean and there are many predictions where they will head, but it’s really impossible to predict if they will hit a city or not, hence all the terrors happening in Florida and the Caribbean and South-East Asia. This is just one example there are more.
that would have to involve gravity of the moon (ping pong forces), basically all planets in closer surrounding not forgetting the different energy bursts the sun spits out resulting in an impossibility for a more presice weather prediction as long as we dont have the sun and its cookings in an entire equation.
to be fair, there are so many micro and macro thermal influences not forgetting that this has a large scale pressure differences in pockets in the air can never be all determined.
those are 2 examples which do not actually exclude that the “solved” equations as we know it may be even correct.
Thermodynamics, Electro-magnetism, Fluid Dynamics are governed by the same Navier-Stokes equations
hopefully 
but it still does not prove enough (at least not in my understanding) that what we know for now is wrong.
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As for the Moon and Sun, this is part of the initial vector field. Assume you know all that. You currently can’t predict the behavior of the fluids down to its infinitesimals in 3D / 4D (assume the time)
Terry Tao has a good article on this:
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so to get a more conclusive picture, the equation can not even be theoretically solved, due to the complexity of the calculation process? so that has nothing to do with the complexity of the circumstances, just the blank theory cant be solved yet, correct?
There is a system of equations not just one.
There may be a missing piece another equation that needs to be added in order to solve the system, so I guess yes.
You know the calculations regarding jet engines and reactive force, is not accurate. The theory there is also not complete.
holistically there is only one 
so i guess it makes no sense to dig further down the rabbit hole, if the geniuses of the world are not smart enough to determine all factors. i certainly will not go there. a pity that you need such a huge repository of knowledge to solve something simple like the flow of fluids.
turbulence is not simple
ok.
so from my understanding, turbulences are abstracted nothing more than this?
and where are the other particles in the fluid? These are not the only one moving in such a case.
i guess not but this is the pinnacle of where the turbulence takes place.
See, I am also concerned with this issue. I want to learn more about it, but vector math is a bitch