## Columbia Mathematics Department
Colloquium

*Wellposedness** of the two and three dimensional*

* full
water wave problem*

### by

### Sijue Wu

### University of Michigan

Abstract:

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**

**Mathematics
520**

**Tea will be
served at 4:30pm**