In preparation for the sections which follow, which deal with the inviscid, non-diffusive case, we restrict our attention to this case for required boundary conditions. There are two types of conditions to be considered: kinematic and dynamic. For a well-posed problem the number of conditions which should be stipulated depends upon the nature of the equations for the interior of the fluid. An ill-posed problem can exist either if there are too few or too many constraints imposed as boundary conditions. The required number for fixed boundaries differs from the number required for a free surface.