I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf
I could not really understand the description. Could someone explain a little bit more?
It says, "For the lid driven cavity problem this means that homogeneous Neumann boundary conditions are prescribe everywhere. This implies in particular that the pressure $P$ is only defined up to a constant, which is fine, since only the gradient of $P$ enters the momentum equation."
What does it mean "only defined up to a constant"? By solving the Poisson equation, you obtain the values of $P$ and can calculate its gradient. The constant means this pressure value? And if it's not "only up to constant", what do we get? derivative or integral?