We consider the question of global in time existence and uniqueness of solutions of the
infinite depth full water wave problem. We show that the nature of the nonlinearity of the
water wave equation is essentially of cubic and higher orders. For any initial data that
is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely
solvable almost globally in time. And for any initial interface that is small in its steepness and
velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.
April 7th, Wednesday, 5:00-6:00 pm
Tea will be served at 4:30pm