  The forces generated by moving interfaces usually include the parts due to
tangential stretching. We derive an evolution equation for the tangential
stretching, which then forms the basis of an Eulerian formulation based on
level set functions. The jump conditions are then derived using the level set
and stretch functions. Compared with the traditional jump conditions under
Lagrangian formulation, the jump conditions under the Eulerian formulation are
compact and clean. The work here makes possible a local level set formulation
for immersed interface method to simulate membranes or vesicles where the
tangential forces are present.
