  We consider the creeping flow of a Newtonian fluid in a hemispherical region.
In a domain with spherical, or nearly spherical, geometry, the solution of
Stokes equation can be expressed as a series of spherical harmonics. However,
the original Lamb solution is not complete when the flow is restricted to a
semi-infinite space. The general solution in hemispherical geometry is then
constructed explicitly. As an application, we discuss the solutions of
Marangoni flows due to a local source at the liquid-air interface.
