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Why the Navier-Stokes equations are so difficult to solve?
yeah they are impossible to solve analytically sometimes...specially when we work on cylinderical and and spherial coordinates
unless we reduce the variables to one or 2 sometimes with some assumptions...
The Navier-Stokes equations describe the behaviour of fluids, which is, even iteratively, difficult to solve. Now, to give a closed-form solution (if at all possible), requires a ridiculous amount of general work. But it's not difficult to see why they are so hard to solve by observing the behaviour of water with any action upon it.