Integration by parts on a family of smooth surfaces evolving by the volume flow motivates a weakly defined volume flow.  We then approximate
the space-time track of a compact initial surface by surfaces  M^e which are minimisers of a certain functional.  Translating the M^e  in the vertical direction approximates the evolution of the M^e  by the weak volume flow.   A compactness result permits us to send  e to zero and obtain existence of a weak flow.
 

Convenors:Klaus Ecker, Alan Pryde