Maria Elena Schonbek

• Many interesting problems arise from the study of the behavior of fluids. From a theoretical point of view Fluid Dynamics works with a well defined set of equat ions for which it is expected to get a clear description of the solutions. Unfortunately, in ge neral this is not easy even if the many experiments performed in the field seem to indicate which path to follow. Some of the basic questions are still either partially or widely open. For example we would like to have a better understanding on : 1. Questions for both bounded and unbounded domains on regularity, uniqueness, long time behavior of the solutions. 2. How well do solutions to the fluid equations fit to the real flow. Depending on the type of data most of the answers to these questions are knonw, when we work in two dimensions. For solutions in three dimensions, in general, we have only partial answers.