Hi, i am not getting the exact reason that why NS equations cannot be solved analytically. that is why cant we obtain a general solution for NS eqns??? is it due to lack in the improvement in mathematics or what???

Two many variables, not enough equations.

Why not enough equations? For 2-D case we have three equations and three unknown (u,v,p). For analytical solution you get bonus in $1 million. Hurry.

Which is why for Hagen-Poisueille and Couette flows, analytical solutions exists. Start introducing turbulence or compressibility, or even (heaven forbid) some complicated geometry, and I'd love to see you derive an analytical solution. You also forgot that time might be an issue.

The problem is not really the number of unkowns, but the non-linearite of the equations due to the convectif term.

The only solution you can find is usually in 2D and canceling the convectif term (poiseuille..etc )or the diffusif term (bernoulli).

well, this is my point of view....

thanks to all

non-linear give the difficulty! that all