DYNAMICS OF CLOSED INTERFACES IN 2-DIMENSIONAL LAPLACIAN GROWTH

We study the process of two-dimensional Laplacian growth in the limit of zero-surface tension for cases with a closed interface around a gro wing bubble (exterior problem with circular geometry). Using the time- dependent conformal map technique we obtain a class of fingerlike solu tions that are characterized by a finite number of poles. We find the conditions under which these solutions remain smooth for all times. Th ese solutions allow the description of the system in terms of a finite number of degrees of freedom, at least in the limit of zero-surface t ension. We believe that, whenever they remain smooth, they can also be used as a nonlinear basis even when surface tension is included.