Why doesn't the Navier-Stokes equation have a solution?

[Sawawdeh]

Why the navier-stokes equation don't have a solution ?

 

[Nugatory]

Why the navier-stokes equation don't have a solution ?

Because it’s hard enough that so far no one has figured it out. Perhaps no one ever will.

Google for “Millennium prize navier-stokes” for more about what has to be figured out.

 

[Chestermiller]

The Navier Stokes equations do have solutions for certain specific flows.

 

[nasu]

If we don't know the solution(s), it does not mean that the equation does not have solutions, does it?

 

[Filip Larsen]

Classically the word solution often refer to a closed form solution, i.e. a "simple" symbolic solution general for large set of initial conditions and parameters, and in that sense we know that there are some (turbulent) flows that cannot have such a solution even if the actual flow dynamics still satisfy the equations.
However, in context of numerical analysis (i.e. in this case computational fluid dynamics) the word solution more imply any possible solutions achievable by numerical means so here it would make sense to say that a specific turbulent flow is a solution to the equations. Since turbulent flows has sensitivity to initial conditions this usually means the numerical solution can only be an approximation that share some statistical measure with the exact solution but also that the two will eventually diverge over time.

 

[sophiecentaur]

@Sawawdeh It's never a surprise when an analytical solution to a problem doesn't exist. We start our Maths and Science education being presented with a number of situations and equations that are soluble analytically and exactly (you have to be encouraged initially) but, once you get into Integral Equations you find that most situations can only be dealt with numerically. In the recent past (pre-digital) people used vast books of tables of integrals to calculate approximate answers for problems.
Then someone discovered Chaos. . . . . .