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The three-dimensional jump conditions for the pressure and velocity fields,up to the second normal derivative,across an incompressible/inextensibleinterface in the Stokes regime are derived herein. The fluid viscosity is onlypiecewise continuous in the domain while the embedded interface exerts singularforces on the surround fluids. This gives rise to discontinuous solutions inthe pressure and velocity field. These jump conditions are required to developaccurate numerical methods, such as the Immersed Interface Method, for thesolutions of the Stokes equations in such situations.

The Three-Dimensional Jump Conditions for the Stokes Equations with Discontinuous Viscosity, Singular Forces, and an Incompressible Interface