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The equations governing the motion of fluids and gases (Navier-Stokes, Euler, etc) have been, since they were first formulated, some of the most challenging problems in mathematics. On all space or periodic domains, many existence and regularity results have been proven, although quite a few results remain open (e.g. the Millenium Problem). When set on arbitrary domains and coupled with boundaries that move with and react to the fluid, few results were known until the last decade, and even short-time existence for many problems is still open. In this talk, I will prove the existence of smooth solutions, for a short time, to the incompressible Navier-Stokes equations with a free boundary, in the case where the fluid has zero surface tension.

Pizza and Soda will be served.