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

Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows