I think Jersey Tom might be pulling your chain a bit there. Those are, I think, just the incompressible equations too, so it can get harder.
Anyway, if you can find a solution to those equations for an arbitrary problem then you'll win a Fields Medal I should think.
If you really want to get a bit more of a grip on fluid dynamics I would start by considering the fundamental phenomena of 'Advection' and 'Diffusion'. These processes are described in the above equations, but also have some fundamental physical meaning.
Here's some quick links to have a look:
There's probably better out there than these, but I'm sure you're better at hyperlinking than me. The introduction to a fluid dynamics text book would inform you at lot also, and give you a peek into the weird world of turbulence.