Understanding Laplace's Equation and the Role of Time in Velocity Potential

[Qyzren]

i'm a little bit confused.
if the velocity potential Φ = Φ(x,y,t).
and it says Φ satifies laplace's equation.
does that mean ∂²Φ/∂x² + ∂²Φ/∂y² = 0
or
∂²Φ/∂x² + ∂²Φ/∂y² + ∂²Φ/∂t² = 0.

does the time variable get included??

i'm thinking it isn't but I'm not exactly sure.

 

[HallsofIvy]

Laplace's equation is
[tex]\frac{\partial^2 \phi}{\partial x^2}+ \frac{\partial^2 \phi}{\partial y^2}= 0[/itex]
. Usually, Laplaces's equation is for functions that are independent of t.