The answer: Kinematic Boundary Condition - specify the flow velocity $\vec{v}$ at the boundaries.

The surface of the body does not allow flow through it. This implies that the difference of the fluid velocity and body surface velocity in the direction normal to the body surface should be zero. This statement is expressed by the equation

$$(\vec{v}-\vec{U}).\vec{n} = 0 \mbox{\ on the body surface,\ } \notag$$

and in terms of the potential function $\phi$ we have

$$\nabla\phi.\vec{n} = \vec{U}.\vec{n} = U_{n} \mbox{\ or\ } \f... ...artial \vec{n}} = U_{n} \mbox{\ on the body surface.\ } \notag$$

The other boundary lies at the infinite (unbounded fluid domain). Far from the body, the fluid is not affected by the body movement, so the velocity field at the infinite should be zero. This is expressed by the equation

$$\vec{v} \rightarrow 0 \mbox{\ as\ } \sqrt{x^{2}+y^{2}+z^{2}} \rightarrow \infty, \notag$$

and in terms of the potential function $\phi$ we have

$$\nabla\phi \rightarrow 0 \mbox{\ as\ } \sqrt{x^{2}+y^{2}+z^{2}} \rightarrow \infty. \notag$$